Blanket Squares are cut on the diagonal to form triangular blanket pieces. The hypotenuse of the resulting triangles is 40 inches long. What is the side length of each piece?(1 point)
Responses
203–√
20 square root of 3
20
20
402–√
40 square root of 2
202–√
The correct answer is 20.
To see why, let's consider a right triangle with legs a and b and hypotenuse c. By the Pythagorean Theorem, we have a^2 + b^2 = c^2.
In this problem, the hypotenuse is given as 40 inches. So let's use a and b to represent the side lengths of each triangular piece.
We have a^2 + b^2 = 40^2.
Since the squares are cut on the diagonal, the resulting triangles are isosceles right triangles. This means that a = b.
Substituting a for b in the equation, we get a^2 + a^2 = 40^2.
Simplifying, we have 2a^2 = 40^2.
Dividing by 2, we get a^2 = 40^2 / 2.
Taking the square root of both sides, we have a = √(40^2 / 2).
Simplifying further, we have a = √(1600 / 2) = √800 = 20√2.
Therefore, the side length of each triangular piece is 20√2 inches.