The width of the rectangle is 5 m less than the length, and the perimeter is 42 m. What is the area of this rectangle?

Let’s compose equations in which we denote the length of the rectangle by x. Then the width of the rectangle is x – 5:

x + x – 5 + x + x – 5 = 42.

We collect x.

4 x – 5 – 5 = 42.

Move the numbers to the right side of the equation, changing their signs to the opposite.

4 x = 42 + 5 + 5.

4 x = 52.

We are looking for an unknown factor:

x = 52/4;

x = 13.

This means that the length of the rectangle is 13 cm.

Then the width of this figure is:

13 – 5 = 8 cm.

Let’s check the correctness of the solution by finding the perimeter.

P = 8 * 2 + 13 * 2 = 16 + 26 = 42.

Everything is correct.