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?(1 point) Responses 14.14 14.14 10 10 28.28 28.28 4.47
Let's call the length of each side of the square x inches.
When the square is cut on the diagonal, it forms 2 right triangles where the hypotenuse of each triangle is 20 inches long.
Using the Pythagorean theorem, we know that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
So, for each triangle, we have:
(x^2) + (x^2) = (20^2)
Simplifying the equation:
2(x^2) = 400
Dividing both sides by 2:
x^2 = 200
Taking the square root of both sides:
x = √200
Simplifying the square root:
x = √(100*2)
x = 10√2
Therefore, the length of each side of the square is 10√2 inches.
Rounded to two decimal places, the answer is 14.14 inches.
So, the correct response is: 14.14 14.14