SOLUTION: A right triangle has 6-inch, 8-inch, and 10-inch sides. A square can be inscribed in this triangle, with one vertex on each leg and two vertices on the hypotenuse. How long are the

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Question 1157507: A right triangle has 6-inch, 8-inch, and 10-inch sides. A square can be inscribed in this triangle, with one vertex on each leg and two vertices on the hypotenuse. How long are the sides of the square?
Answer by greenestamps(13195) About Me  (Show Source):
You can put this solution on YOUR website!



The diagram shows the right triangle with AB=10, AC=6, and BC=8.

The inscribed square divides triangle ABC into three triangles and the square; each of the triangles is similar to triangle ABC.

So in each of the small triangles, the ratio of the side lengths is 3:4:5.

If x is the side length of the square, then hypotenuse AD of triangle AGD is (5/4)x, and leg DC of triangle DCE is (3/5)x.

But we know AC is 6, so

%285%2F4%29x%2B%283%2F5%29x+=+6
%2825%2F20%29x%2B%2812%2F20%29x+=+6
%2837%2F20%29x+=+6
x+=+6%2F%2837%2F20%29+=+6%2A20%2F37+=+120%2F37