Final answer:
To find the perimeter of a square given its diagonal, we can use the Pythagorean Theorem to find the length of one side. The perimeter of the square is then 4 times the length of one side.
Step-by-step explanation:
To find the perimeter of a square when the diagonal is given, you can use the Pythagorean Theorem. In a square, the diagonal is the hypotenuse of the right triangle formed by two sides. Let's assume the length of one side of the square is x. According to the Pythagorean Theorem, (x^2) + (x^2) = (10√2)^2.
Simplifying the equation, 2x^2 = 200. Dividing both sides by 2, we get x^2 = 100. Taking the square root of both sides, x = 10.
Since all sides of a square are equal, the perimeter of the square is 4 times the length of one side. Therefore, the perimeter of the square is 4 * 10 = 40 units.
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