The perimeter of a rectangle is 40 cm, what is the area of a rectangle if the length is 9 times the width?

First of all, let’s calculate what the sum of the length and width of the rectangle is equal to, for which we divide the perimeter known from the problem statement in half:

40: 2 = 20 (cm).

It is also known from the condition of the problem that the length is 9 times greater than the width, that is, the length together with the width represent 10 parts, where 9 parts are for the length, and one part for the width. Thus, we find what is 1 part, dividing the sum of the length and width by the number of parts:

20: 10 = 2 (cm).

The width of the rectangle is 2 cm.

Let’s find its length: 2 * 9 = 18 (cm).

We calculate the area of ​​this rectangle by multiplying the length by the width:

S = 2 * 18 = 36 (cm²).

Answer: 36 cm².