If the perimeter of a square is 68 ft, find the approximate length of its diagonal.

If the perimeter of a square is 68 ft, find the approximate length of its diagonal.

17 ft

24 ft

48 ft

38 ft

1 answer

The perimeter of a square is given by P = 4s, where s is the side length of the square. Given that the perimeter is 68 ft, we can set up the equation:

68 = 4s

Dividing by 4 on both sides, we get:

s = 17 ft

To find the diagonal of a square, we can use Pythagoras' Theorem. The diagonal of a square divides the square into two right-angled triangles.

Let d be the length of the diagonal and s be the side length. Then, using Pythagoras' Theorem:

d^2 = s^2 + s^2 = 2s^2

Substitute s = 17 ft:

d^2 = 2(17)^2 = 2(289) = 578

Taking the square root of both sides:

d = sqrt(578) ≈ 24 ft

Therefore, the approximate length of the diagonal of the square is 24 ft.

Answer: 24 ft