Question

Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary.(1 point)Responses
4
2.83
8
4.24

Answer 1

To find the length of the diagonal of a square using the Pythagorean theorem, we can use the formula c^2 = a^2 + b^2, where c is the length of the diagonal and a and b are the lengths of the sides of the square.

Since a square has equal sides, let's assume the length of one side is x. Then, we have:

c^2 = x^2 + x^2

Simplifying, we get:

c^2 = 2x^2

Taking the square root of both sides to solve for c, we have:

c = √(2x^2)

Now, let's substitute the given values:

c = √(2 * 4^2) = √(2 * 16) = √32 = 4.24

Therefore, the length of the diagonal of the square is approximately 4.24.