the perimeter of a square is 64 ft. find the length of a diagonal.
64/4 = 16 ft on each side
Use the Pythagorean Theorem to find the length of the diagonal.
To find the length of the diagonal of a square, we can use the Pythagorean theorem.
Step 1: Find the length of one side of the square.
Since the perimeter of the square is given as 64 ft, and a square has four equal sides, we can calculate the length of one side by dividing the perimeter by 4.
Perimeter = 4 * side length
64 ft = 4 * side length
Divide both sides of the equation by 4 to find the side length.
64 ft / 4 = side length
16 ft = side length
Step 2: Use the Pythagorean theorem to find the length of the diagonal.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In the case of a square, the diagonal is the hypotenuse.
Let's call the side length of the square "s" and the length of the diagonal "d". Applying the Pythagorean theorem:
s² + s² = d²
2s² = d²
Now, substitute the value of the side length we found earlier (16 ft) into the equation:
2(16 ft)² = d²
2 * 256 ft² = d²
512 ft² = d²
Taking the square root of both sides gives us:
sqrt(512 ft²) = sqrt(d²)
sqrt(512 ft²) = d
d ≈ 22.63 ft
Therefore, the length of the diagonal of the square is approximately 22.63 ft.