A square's perimeter measures the entire outside of the square, combining all four sides into a single linear measurement. The diagonal of a square connects opposite corners, measuring the distance between them and cleaving the square into two identical isosceles right triangles. Since the diagonal doubles as a hypotenuse, it carries the same quality as isosceles right triangle's hypotenuse by being √2 --- or approximately 1.414 --- times greater than one of the square's sides. With this property, and the fact that the perimeter is four times the size of one side, finding the length of a square's diagonal is just a matter of simple division and multiplication.
Instructions
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1
Write down the square's perimeter. For this example, allow the square's perimeter to be 20 inches.
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2
Divide the perimeter by 4 to calculate the length of one of the square's sides. In this example, dividing 20 inches by 4 equals 5 inches.
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3
Multiply a side's length by √2 to calculate the square's diagonal. Concluding this example, 5 multiplied by √2 equals approximately 7.017 --- the square's diagonal is 7.017 inches.