A square is inscribed in a right isosceles triangle such that one side of the square lies on the hypotenuse. If the hypotenuse has length 12, what is the side length of the square?
Answer and explanation
Correct answer: A. 4
- Step 1: In a right isosceles triangle with hypotenuse c = 12, the altitude to the hypotenuse is h = c / 2 = 6.
- Step 2: Let x be the side length of the square sitting on the hypotenuse.
- Step 3: The triangle above the square has base x and height 6 - x, and is also a right isosceles triangle.
- Step 4: In that smaller top triangle, the altitude is half its hypotenuse: 6 - x = x / 2.
- Step 5: Multiply by 2: 12 - 2x = x, so 3x = 12, giving x = 4.
Answer
4.
Why not the others: 3 assumes 4*x = 12; 6 is the altitude of the triangle; 4.5 is an approximation.
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