Final answer:
To find the diagonal of a square, use the Pythagorean theorem. In this case, the length of the diagonal is approximately 11.31 inches.
Step-by-step explanation:
To find the length of the diagonal of a square, we can use the Pythagorean theorem. 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 other two sides.
In a square, the diagonal is the hypotenuse of a right triangle formed by the two sides. Let's call the side length of the square 's' and the length of the diagonal 'd'.
Using the Pythagorean theorem, we have:
d^2 = s^2 + s^2 = 2s^2
The perimeter of a square is given by 4s, and we are given that the perimeter is 32 inches. So we can set up the equation:
4s = 32
From this equation, we can solve for 's':
s = 8
Now, substitute the value of 's' back into the equation for the diagonal:
d^2 = 2(8)^2 = 128
Taking the square root of both sides,
d = sqrt(128)
Therefore, the length of the diagonal is approximately 11.31 inches.