One side of the rectangle is 7 cm less than the other, and the diagonal of the rectangle is 17 cm.

One side of the rectangle is 7 cm less than the other, and the diagonal of the rectangle is 17 cm. Find the perimeter of the rectangle.

From the condition it is known that one side of the rectangle is 7 cm less than the other, and the diagonal of the rectangle is 17 cm.In order to find the perimeter of the rectangle, we apply the formula:
P = 2 (a + b).
We need to find the sides of the rectangle. To do this, we will consider a right-angled triangle formed by the sides of the rectangle and the diagonal.
Let’s denote by x cm the length of one of the sides and (x – 7) cm the length of the second side.
We apply the Pythagorean theorem: a ^ 2 = b ^ 2 + c ^ 2;
x ^ 2 + (x – 7) ^ 2 = 17 ^ 2;
x ^ 2 + x ^ 2 – 14x + 49 = 289;
2x ^ 2 – 14x – 240 = 0;
x ^ 2 – 7x – 120 = 0;
D = 49 + 480 = 529;
x1 = (7 + 23) / 2 = 15;
x2 = (7 – 23) / 2 = -8 root does not fit.
The large side of the rectangle is 15 cm, and the smaller side is 15 – 7 = 8 cm.
P = 2 (15 + 8) = 2 * 23 = 46 cm.