If the perimeter of a square is equal to 5x + 1 and the length of the diagonal of the square is (2x – 2)√2, what is the length of a side of the square?

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Accepted Answer

The diagonal of a square is the hypotenuse of an isosceles right triangle, since the 4 angles of a square are right angles, and the sides of a square are all congruent to each other. Therefore, the measure of a side of the square is equal to the measure of the diagonal divided by √2: (2x – 2)√2 ⁄ √2 = 2x – 2 units. Therefore, the perimeter of the square, 5x + 1, is equal to 2x – 2 + 2x – 2 + 2x – 2 + 2x – 2 = 8x – 8; 8x – 8 = 5x + 1, 3x = 9, x = 3. The length of a side of the square is equal to 2(3) – 2 = 6 – 2 = 4 units.

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