A square is inscribed in a right triangle. The legs of the triangle are 2 and 3. Find the side length of the square.
+128460 We can use similar triangles to solve this....see the following image
Let AD be one side of the square
And let DE be the other side of the square
And using similar riangles, we have that triangle BDE is similar to triangle BAC
So
BD/ DE = BA/ AC
BD/ DE = 2 / 3
But DE = AD
So
BD / AD = 2/3
BD : AD = 2 : 3
So there are 5 equal parts of AB and AD is 3 of them...so AD = (3/5)(AB) = (3/5)(2) = 6/5 = side of the square
