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
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