SOLUTION: A square is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse and two other on the legs. Find the length of the side of the square, if th

Question 1028619: A square is inscribed in a right isosceles triangle, such that two of its vertices lie on the hypotenuse and two other on the legs. Find the length of the side of the square, if the length of the hypotenuse is 3 inches.
Include formal proof as well!!
So I know that the answer is 1 inch, but I don't know how to PROVE IT. Thank you!!
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Let the side length of the square be s. The triangular regions outside the square are all isosceles right triangles, so you can work out that there are many segments of side length s. In particular, the two vertices of the square trisect the hypotenuse, and the length of the hypotenuse is s+s+s = 3, or s = 1.

It is a little difficult to explain in words, but draw it out and you should figure it out.
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