a) Maria walked 420m.

This is a place for the community of learners in Room 8-16 to learn and enjoy math. It is an extension of the classroom making it accessible 24 hours a day, 7 days a week.

## Thursday, November 18, 2010

### Jocelle Garcia's scribe post

a) Maria walked 420m.

### Jayvee's Pythagoras Scribe Post

Could these measurements form a rectangle? Justify your answer.

a²+b²=c²

22²+9²=c²

(22x22)+(9x9)=c²

484cm2+81cm 2=565

√565cm²≠ 566.44

This can't form a rectangle because a and b does not equal c.

7.What is the height of the wheelchair ramp? Give your answer to the nearest tenth of a centimetre.

a²=c²-b²

80²-79²=a²

6400-6241=159

159cm²=a²

√159cm=√a²

12.6cm²=a

The height of the wheelchair ramp is 12.6cm.

13.A cruise ship travels from Port Cassett north at a speed of 34 km/h for 2.5 h. Then it turns 90° and travels west at 30 km/h for 7.3 h. When it reaches Green Sea Island, how far is the ship from Port Cassett? Express your answer to the nearest kilometre.

a²+b²=c² 34x2.5=8.5

219²+8.5²=c² 30x7.3=219

(219x219)+(8.5x8.5)=c2

47961+72.25=48033.25

48033.25km=c²

√48033.25km=√c2

219.16km=c

The ship is 219.16km away from Port Cassett.

## Wednesday, November 17, 2010

### Carl's Homeworkbook Scibe Post

### Nikki's Pythagoras Scribe Post

answer The are for A (6cm) is 36 cm2. B (8cm) is 64 cm2.

b) What is the area for the square attached to the hypotenuse?

The answer is, The are for the hypotenuse is 100cm

c) What is the length of the hypotenuse?

The length for the hypotenuse is 10cm2.

8)The side view of a ramp at the Grocery store is in the shape of a right triangle. Determine the length of a ramp, to the nearest centimeter.

a2+b2=c2

502+2002 =c2

(50 times 50)+(200 times 200)=c2

2500+40000=c2

42500=c2

206=c

11)The right triangle below has a square attached to the hypotenuse. What the perimeter of the triangle. Give your answer to the nearest centimeter.

The answer is 72.2

14) What are the length of b and c?Write your answer to the nearest tenth of a meter where appropriate.

The length for b is 4m. The length for c is 7.2.

## Tuesday, November 16, 2010

### Textbook work

**#6 - Determine the length of the leg for each triangle.**

6 a)-

c² - a² = b²

25² - 7² = b²

625 cm² - 49 cm² = b²

576 cm² = b²

√576 cm² = √b²

24 cm = b

6 b)-

t² - s² = r²

26² - 24² = r²

676 cm² - 576 cm² = r²

100 cm² = r²

√100 cm² = r²

10 = r

**#9 -Tina wants to construct a path along the diagonal of her yard. What length will the path be? Express your answer to the nearest tenth of a metre.**

a² + b² = c²

6² + 12² = c²

36 m² + 144 m² = c²

180 m² = c²

√180 m² = √c²

13.4 m = c

The length of the path will be 13.4 m long

**#12-The hypotenuse of the triangle cuts the circle in half. What is the diameter of the circle? Express your answer to the nearest tenth of a centimetre.**

a² + b² = c²

7² + 5² = c²

49 cm² + 25 cm² = c²

74 cm² = c²

√74 cm² = √c²

8.6 cm=c

The diameter of the circle is 8.6 cm

**#15- The coordinate grid shown was drawn on centimetre grid paper. What is the length of line segment AB? Express your answer to the nearest tenth of a centimetre.**

a² + b² = c²

4² +2² = c²

16 cm² +4 cm² = c²

20 cm² = c²

√20 cm² = √c²

4.5 cm = c

The line segment is 4.5 cm.

Homework!! - Pages 30 and 31 in the homework book

### Using the Pythagorean Relationship

Okay,so I'm doing odds,and I think Karen is doing evens.

Pg.30-31

1.The Pythagorean relationship can be used to determine the length of the hypotenuse of a right triangle when the lengths of the two legs are known. AGREE?

3.Determine the length of the hypotenuse.Show your work.

a)

k² + j² = l²

40cm² + 9cm² = l²

(40² x 40²) + (9² x 9²) = l²

1600cm² + 81cm² = 1681cm²

√1681cm² = √l²

41cm²

b)

p² + q² = r² 12m² + 35m² = r² (12² x 12² ) + (35² + 35²) = r²

144m² + 1225m² = 1369m²

√1369m² = √r²

37cm²

5.Calculate the missing side length for each right triangle,to the nearest tenth of a centimeter.Show your work.

a)

w² + x² = y²

w² + 25² = 36²

11 = 25 - 36

√11 = 3.3

3.3²

b)

f² + g² = h²

7cm² + g² = 12cm²

49cm² + g² = 144cm²

144cm² - 49cm² = 95cm²

√95cm² = 9.7cm²

9.7cm²

7.A triangle is made up of two smaller congruent right triangles.

a)Find the Length of the hypotenuse for the right triangle,to the nearest tenth of a metre.Show your work.

4m² + 2m² = b²

(4 x 4) + (2 x 2) = b²

16m² + 4m² = b²

√20m² = 4.5m

b = 4.5m

b)Calculate the perimeter of the large triangle,to the nearest tenth of a metre.Show your work.

I don't know how to do this one..Help?

### Karen's Scribe Post

a)

c² + 24² = 26²

c² + 576 =676

c² + 576 - 576 = 676 - 576

c² = 100

c = √100

c = 10m

b)

b² + a² = c²

b² + 15² = 39²

b² + 225 = 1521

b² + 225 - 225 = 1521 - 225

b² = 1296

b = √1296

b = 36cm

a)

c² = a² + b²

c² = 8² + 9²

c² = 64 + 81

c = √145

c = 12cm (nearest centimeter)

b)

c² = a² + b²

c² = 6² + 10²

c² = 36 + 100

c = √136

c = 12cm

6. Find the height of a triangle with a base of 4 cm and a hypotenuse of 11 cm. Round to the nearest tenth of a centimeter. Show your work.

a² + b² = c²

a² + 4² = 11²

a² + 16 = 121

a² + 16 -16 = 121 - 16

a² = 105

a² = √105

a = 10.2cm

8. Ellie and Lucas are going the skateboard park to try out the new ramp. Is the new ramp a right triangle? Explain your thinking.

a² + b² = c²

2² + 3² = 5²

4 + 9 = 13

13 ≠ 15 (5²)

No, it is not a right triangle because it doesn't equal the hypotenuse/5².

### Lizelle's Scribe

Question 7

What is the missing length of the leg for each triangle? Give your answer to the nearest tenth of a millemetre.

My formula is:

h= i-g=h

h=9-5=4

h=4

What is the minimum distance the plaer at third base has to throw the ball to the runner out at first base? Express your answer to the nearest tenth.

a²+b²=c²

27²

## Monday, November 15, 2010

### Using The Phythagorean Relationship.

The following picture shows the line from 2nd to home making a right triangle.

a2+ b2= c2

(27x27) + (27x27) = c2

729m(squared) + 729m(squared) = c2

1458= c2

✔1458cm(squared)= ✔c2

38.18m= c

The following picture shows a right triangle. Find h/ c .

a2 + b2= c2

(6x6) + (10x10) = c2

36cm(squared) + 100cm(squared)= c2

136cm2= c2

✔136cm(squared) =✔c2

11.66cm= c

The following picture shows a right triangle. You are only given r & t. Find s.

a2 + b2 = c2

20(squared) + b2= 52(squared)

(20x20) + b2 = (52x52)

b2= 52(squared) - 20(squared)

b2= 2704- 400

b2= 2304 cm(squared)

✔ b2= ✔2304

b= 48cm

The following picture shows a right triangle. You are only given b and c. Find a.

a2 = c2 - b2

a2 = 9(squared) - 4(squared)

a2= 81cm2 - 16cm2

a2= 65cm

✔a2= ✔65cm

a= 8.06 cm

HOMEWORK :)

Page 103 and 104 .

Questions 1, 2, 3 and 4.

Question 1:

Jack must determine the side length of a right triangle. He decides to draw it, and then measure it, as shown. Do you agree with the method that Jack is using? Explain .

I agree with the method Jack is using, because once he knows what the two side lengths are, he can find the hypotenuse.

Question 2:

Kira calculated the missing side length of the right triangle.

Is Kira correct ? If she is correct, explain how you know. If she is incorrect, explain the correct method.

Kira is not correct, because she forgot to do this part:

194cm(squared) = y2

✔194= ✔c2

13.9= c

## Tuesday, November 9, 2010

### Nicholas's Scribe Post.

7.11 x 11 = 121 12 x 12 = 144

122-143

8.2 x 2 = 4 3 x 3 = 9

5-8

### Filimon Scribe Post

### Ishaka's square roots scribe post

a) 72

square root 64 =8 x 8

square root 72 = 8.__x 8.__

square root 81 = 9 x 9

I estimated that 8.49 was the square root of 72 calculator 8.48

b) 103

square root 100 = 10 x 10

square root 103 = 10.__ x 10.__

square root 121 = 11 x 11

I estimated that 10.15 x 10.15 was the square root of 103 calculator 10.14

c) 55

square root 49 = 7 x 7

square root 55 = 7.__ x 7.__

square root 64 = 8 x 8

I estimated that 7.42 x 7.42 was the square root of 55 calculator 7.41

6) What is an example of a whole number that has a square root between 9 and 10?

9 10

81 100

examples: 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99.

### Victoria's Square Root Post

Stella is planning an outdoor wedding. She would like a square dance ﬂoor with an area of 115 m2.

a) Determine the side length of the dance ﬂoor, to the nearest tenth of a metre.

b) Stella ﬁnds out that the dance ﬂoor will be made up of ﬂoorboards that each measure 1 m2. What are the two side lengths the dance ﬂoor can have that are closest to what she wants?

c) What are the two square areas for the dance ﬂoor that Stella can choose from?

d) Which area will Stella choose? Explain.

Answers !

a.)10.7m b.) Sorry i dont know this question c.)100m2 or 121m2 d.) She will chose the 121m2 dance floor because its closer to the size she wanted.

New Question !

14. Alex is thinking of a number.

a) What number could he be thinking of?

b) Is there more than one answer? Explain

Answers!

a.) 60 b.) No, there is only one answer and the nember must be between 49 and 64. The only multiple number is 12m this is the range of 60.

### Richards Scribe Post

16.a) 27m squared b) i cant find the answer . can you try finding the answer by commenting.

17.a) 324cm squared b)1296cm squared c) 36cm by 36cm squared

### Kevin's Square Root Scribe Post

**Show you know:**

a) Identify a whole number with a square root between 8 and 9.

b) How many whole numbers can you find that have a square root between 8 and 9? show you work.

a) First I changed the number 8 to 64 (8x8) and 9 to 81 (9x9).

64 ? 81

64 73 81

b) There are 16 whole numbers I found.

65 = 8.0

66 = 8.12

67 = 8.18

68 = 8.24

69 = 8.30

70 = 8.36

71 = 8.42

72 = 8.48

73 = 8.54

74 = 8.60

75 = 8.66

76 = 8.71

77 = 8.77

78 = 8.83

79 = 8.88

80 = 8.94

I used perfect squares to find these.

P.s I'm not sure if I'm right so can you guys help me out? Just post your answers at the comment section and I'll take a look at them.

### Nikki's Math Post

19.) Estimate 160 100. Explain how you determined your estimate.

## Monday, November 8, 2010

### Victoria's Pythagoras Post

### Justin's Square Root Scribe Post

For each number of the following, use perfect squares to estimate the square root to one decimal place.Check your answers with a calculator

a) ✔18 b) ✔23 c) ✔35

You can estimate using perfect squares to find the square root to one decimal place like this:

✔18 is in between the perfect numbers 16 and 25. ✔16=4x4 ✔18=4.__ ✔25=5x5

✔18=4.__ because if you multiply 4.__ it equals 18.

✔23 is in between the perfect numbers 16 and 25. ✔16=4x4 ✔23=4.__ ✔25=5x5

23=4.__ because if you multiply 4.__ it equals 23.

✔35 is in between the perfect numbers 25 and 36. ✔25=5x5 ✔35=5.__ ✔36=6x6

35=5.__ because if you multiply 5.__ it equals 35.

## Sunday, November 7, 2010

### Paulo's Pythagoras Scribe Post

a) What is the area of each square attach to the three sides of the right triangle?

81 cm2 and 144cm2

b) Write an addition statement showing the relationship between the areas of the three squares?

81+144=225

c) Describe, using words and symbols, the relationship between side lengths of each square?

PLEASE HELP ME DESCRIBE THE RELATIONSHIP BETWEEN THE SIDE LENGTHS OF EACH SQUARE

14) Show weather each triangle in the table is a right triangle.

Triangle Side Lengths (cm)

A 9,12,15

B 7,8,11

C 7,24,25

D 16,30,34

E 10,11,14

Answer :

A is a right triangle :9 square + 12 square= 15 square

B is not a right triangle :7 square + 8 square= almost 11 square

C is a right triangle : 7 square + 24 square = 25 square

D is a right triangle : 16 square + 30 square= 34 square

E is a right triangle : 10 square + 11 square = almost 14 square

18) The diagram is made of two right triangles and five squares.

PLEASE HELP ME GET THE ANSWER

### Glenn's Pythagoras Scribe Post

a) 30x30= 900mm

### Cathlene's Pythagoras Scribepost

c. Write an addtion statement with the areas of the three squares

The triangle is a right angle because both the legs of the triangle is equal to the area of the hypotenuse.

### Sam's Pythagras Scribe post

3. Kendra is wrong because 'p' is the hypotenuse.

8. If the triangle shown in the text book is a right angle than hypotenuse should be 60cm² because 20cm²+40cm² =60cm² .

11. a² + b² = c²

(6x6) + (5x5) = 8x8

36cm² + 25cm² = 61cm²

61cm² = 64cm²

-Since 61cm² does not equal 64cm² it is not a right triangle.

16. a² + b² = c²

(12x12) + (20x20) = c²

144cm² + 400cm² = 544cm²

√544cm² = 23.32cm

-Baldeep can be sure his box can be square by measuring the hypotenuse.

### Alec's Pythagoras Scribe Post

g. 50x50= 2500mm

f. 40x40= 1600mm

The area of e. is 900 square millimeters

The area of g. is 2500 square millimeters

The area of f. is 1600 square millimeters

9. a) 4x4=16 square cm.

2x2= 4 square cm.

3x3=9 square cm.

b) This is not a right triangle because 2 squared + 3squared doesn't equal 4 squared

12. a) a. squared + b. squared = c. squared

20 + 32 = 52 square cm.

b) a. squared + b. squared = c. squared

100 + 576 = 676 square mm.

c) c. squared - b squared = a. squared

90 - 25 = 65 square cm.

When the hypotenuse is there but one of the leg is missing, I figure it out that when you subtract the one of the legs to the hypotenuse, you will get the missing leg.

d) a. squared + b. squared = c. squared

12 + 12 = 24 square cm.

17. a) a. squared + b. squared = c. squared

21 squared + 28 squared = c .squared

441 + 784 = 1225 square cm.

b) a. squared + b. squared = c. squared

12 squared + 5 squared = c.squared

144 + 25 = 169 square cm.

### Ryan's Pythagoras Scribepost

**5.**A right triangle has side lengths of

**40mm**,

**75mm**, and

**85mm**.

**a)**Sketch the triangle. Draw a square on each side of the triangle.

**b)**What are the areas of the three squares?

**square a**, is

**1,600mm2 (squared)**.

**square b**, is

**5,625mm2 (squared)**.

**square c**, is

**7,225mm2 (squared)**.

**c)**Write an addition statement with the areas of the three squares.

**7,225mm(squared)=7,225mm(squared)**

**10.**A triangle has side lengths of

**120mm**,

**160mm**, and

**200mm**. Is the triangle a

*? Explain your reasoning.*

**right triangle**

*Yes*, this is a right triangle because the sum of the area of each leg, is

**to the area of the hypotenuse.**

*equal***40,000(squared)=40,000(squared)**

**15.**Construction workers have begun to dig a hole for a swimming pool. They want to check that the angle they have dug is

*90 degrees*. They measure the diagonal as shown to be

**9.5m**. Is the angle 90 degrees? Explain your reasoning.

*No*, the angle is not 90 degrees because the sum of the area of each leg, is

**to the area of the hypotenuse.**

*not equal*

**19.**A

*right triangle*has a square attached to each side. Two of the squares have areas of

**10cm(squared)**and

**15cm(squared)**. What are the possible areas for the third square? Draw a sketch for each solution.

**only one possible area**for the third square, and that is the sum of the area of each leg:

**25cm(squared)**. There is only one possible area because it is a

**.**

*right triangle*