Question

The perimeter of a square is 36 inches. Find the length of a diagonal. Round your answer to the nearest tenth.

Answer 1

To find the diagonal of a square with a perimeter of 36 inches, calculate the side length as 9 inches and apply the Pythagorean theorem, resulting in a diagonal length of approximately 12.7 inches.

Step-by-step explanation:

The perimeter of a square is given as 36 inches, so to find the length of one side, we divide the perimeter by 4, since a square has four equal sides. Therefore, each side of the square is 36 inches ÷ 4 = 9 inches. To determine the length of the diagonal, we can apply the Pythagorean theorem in the square. The square's diagonal splits it into two right triangles, each with legs equal to the side of the square. If we denote the length of the diagonal as d and one side as s, the formula d² = s² + s² applies.

With both sides being 9 inches, this becomes d² = 9² + 9², leading to d² = 81 + 81 = 162. Taking the square root to find d, we get d = √162, which is approximately 12.7 inches when rounded to the nearest tenth.

Answer 2

12.7

Step-by-step explanation:

The diagonal formula is x*sqrt(2) with x being one side length.

To find the side length divide the perimeter by 4.

That gives us 9.

Then, all you have to do is multiply that by the square root of 2 and then round.