Apply the Pythagorean Theorem to find the length of the diagonal of the square. Round your answer to the nearest hundredth, if necessary
The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In a square, all sides are equal in length. Let's assume the length of each side of the square is 's'.
To find the length of the diagonal of the square, we need to find the length of the hypotenuse of a right triangle formed by two adjacent sides of the square.
Using the Pythagorean Theorem:
Hypotenuse^2 = Side^2 + Side^2
Hypotenuse^2 = s^2 + s^2
Hypotenuse^2 = 2s^2
Taking the square root of both sides:
Hypotenuse = ā(2s^2)
Hypotenuse = sā2
To find the length of the diagonal, we need to find the length of the hypotenuse. By substituting 's' with the given length of a side of the square and rounding the answer to the nearest hundredth, we can find the length of the diagonal.