Problem 23 · 2022 Math Kangaroo
Stretch
Geometry & Measurement
area-fractionpythagorean-triple
One square is drawn inside each of the two congruent isosceles right-angled triangles. The area of square P is 45 units. How many units is the area of square R?
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Answer: B — 40
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Hint 1 of 2
The two inscribed squares sit differently: one leg-aligned, one tilted on the hypotenuse.
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Hint 2 of 2
There is a fixed ratio between the two square areas for the same right isosceles triangle.
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Approach: use the known ratio of the two inscribed-square areas
- For an isosceles right triangle, the leg-aligned square and the hypotenuse-tilted square have a fixed area ratio of 9 : 8.
- Square P (leg-aligned) has area 45, so the tilted square R has area 45 * 8/9.
- That gives area of R = 40.
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