For this blog I will be showing questions 5, 10, 15, and 19.
5. A right triangle has side lengths of 40 mm, 75 mm, and 85 mm.
a) Sketch the triangle. Draw a square on each side of the triangle.
b) What are the areas of the three squares?
c) Write an addition statement with the areas of the three squares.
b) Area of 40 (a) is 1600 mm² Area of 75 (b) is 5625 mm² Area of 85 (c) is 7225 mm² c) a² + b² = c² 40² + 75² = c² 1600 + 5625 = c² 7225 mm² = c² 7225 square root is 85mm = c
10. A triangle has side lengths of 120 mm, 160 mm, and 200 mm. Is the triangle a right triangle? Explain your reasoning.
Yes this triangle is indeed a right triangle. Due to the fact that a²+b²= c² you add the sums of the smallest squares (120mm and 160mm) which should equal the area of the largest square.
e.x. 120² + 160² = 200² 14,400 + 25,600 = 40,000
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°. They measure the diagonal as shown to be 9.5 m. Is the angle 90°? Explain your reasoning.
No the angle is not 90°. For the it to be 90° the diagonal line would have to be 10m. e.x. 6² + 8² = c² 36 + 64 = c² 100² = c² square root 100 = 10 / square root c² = c
19.A right triangle has a square attached to each side. Two of the squares have areas of 10 cm² and 15 cm². What are possible areas for the third square? Draw a sketch for each solution.
Possible areas for the third square include 5cm² and 25cm² (I got 5 from subtracting 10 from 15 and I got 25 from adding 10 and 15.)
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