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?

The area for square a, is 1,600mm2 (squared).

The area for square b, is 5,625mm2 (squared).

The area for square c, is 7,225mm2 (squared).

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

a(squared)+b(squared)=c(squared)

40(squared)+75(squared)=85(squared)

1,600(squared)+5,625(squared)=7,225(squared)

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

10. A triangle has side lengths of 120mm, 160mm, and 200mm. Is the triangle a right triangle? Explain your reasoning.

Yes, this is a right triangle because the sum of the area of each leg, is equal to the area of the hypotenuse.

a(squared)+b(squared)=c(squared)

120(squared)+160(squared)=200(squared)

14,400(squared)+25,600(squared)=40,000(squared)

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 not equal to the area of the hypotenuse.

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.

There is 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.