The perimeter of the rectangle is 22 and the diagonal is √65. Find the area of this straightforward.

The square of the diagonal of a rectangle is equal to the sum of the squares of two adjacent sides:

d ^ 2 = a ^ 2 + b ^ 2;

a ^ 2 + b ^ 2 = (√65) ^ 2 = 65.

The sum of two adjacent sides of a rectangle is half the perimeter:

a + b = 22/2 = 11.

Squaring both sides of the equality, we get:

(a + b) ^ 2 = 112;

a ^ 2 + b ^ 2 +2 * a * b = 121;

65 + 2 * a * b = 121;

2 * a * b = 121 – 65 = 56;

a * b = 56/2 = 28.

The area of a rectangle is equal to the product of the lengths of two adjacent sides:

S = a * b = 28.