Find the area of a rectangle if its perimeter is 80 and the difference between the larger and smaller sides is 6.

It is known from the condition that the perimeter of the rectangle is 80, and the difference between the larger and smaller sides is 6. In order to find the area of the rectangle, we need to know the lengths of the sides of the rectangle.

Let’s compose and solve a linear equation with one variable.

Let the length of one of the sides be x, then the length of the second side (x + 6).

Formula for finding the perimeter:

P = 2 (a + b);

2 (x + x + 6) = 80;

2x + 6 = 40;

2x = 40 – 6;

2x = 34;

x = 17.

One side is 17, and the other is 17 + 6 = 23.

We are looking for an area using the formula:

S = a * b = 17 * 23 = 391 sq. units