A square is cut on the diagonal to form 2 right triangles. The hypotenuse of the resulting triangles is 20 inches long. What is the length of each of the sides?
Let the side length of the square be denoted by s.
Since the square is cut on the diagonal, the hypotenuse of each right triangle is s inches long.
According to the Pythagorean theorem, in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Therefore, we have:
s^2 + s^2 = 20^2
2s^2 = 400
Dividing both sides by 2, we get:
s^2 = 200
Taking the square root of both sides, we have:
s = √200 = 10√2
Thus, the length of each side of the square is 10√2 inches.