Question

a square is inscribed in a right triangle with side lengths 3, 4, and 5, as shown below. find the side length of the square.

Answer 1

The side of the square is approximately 1.7

How to find the side of the square

Drawing a diagonal (BD) on the square will result to similar triangles with proportions as follows

BD / BA = BC / AC

BD / 3 = 4 / 5

BD = 12/5 = 2.4

And diagonal of a square is x√2

x√2 = 2.4

x = 2.4 / √2

x = 1.697

The side of the square is approximately 1.7