Find the area of a rectangle if its perimeter is 74 and the difference in sides is 17.

We are given a rectangle, the perimeter of which is 74, and the difference of the sides is 17. In order to find the area of the rectangle, we must first find its sides.

To do this, we will compose and solve the equation. Let us denote one of the sides by the variable x, then the other side can be written as (x + 17).

The perimeter of the rectangle is calculated by the formula:

P = 2 (a + b);

2 (x + x + 17) = 74;

2x + 17 = 37;

2x = 37 – 17;

2x = 20;

x = 10 is one of the sides of the rectangle, then the second side is 10 + 17 = 27.

We look for the area of the rectangle by the formula:

S = a * b = 10 * 27 = 270 sq. units.