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 10 10 28.28 28.28 14.14 14.14 4.47
Let's denote the length of each side of the square as x.
Since the square is cut on the diagonal, the hypotenuse of the resulting right triangles will be the diagonal of the square, which is x√2.
Given that the hypotenuse of each triangle is 20 inches, we have:
x√2 = 20
To find x, we can divide both sides of the equation by √2:
x = 20/√2
Multiplying the numerator and denominator of the right side by √2, we get:
x = (20√2)/(√2*√2)
Simplifying the denominator:
x = (20√2)/2
Simplifying further:
x = 10√2
So the length of each side of the square is 10√2 inches.
To convert this to decimal approximation, we can evaluate 10√2 using a calculator:
10√2 ≈ 14.14
Therefore, the length of each side of the square is approximately 14.14 inches.
The correct answer is 14.14 14.14 4.47.