Find the area of a rectangle if its perimeter is 20. and one side is 6 larger than the other.

Let us denote the lengths of the sides of the rectangle through x and y.

According to the condition of the problem, the perimeter of this rectangle is 20, therefore, we can write the following relationship:

x + y = 20.

It is also known that one side of a given rectangle is 6 larger than the other, therefore, we can write the following ratio:

x = y + 6.

We solve the resulting system of equations. Substituting into the first equation the value x = y + 6 from the second equation, we get:

y + 6 + y = 20;

2y + 6 = 20;

2y = 20 – 6;

2y = 14;

y = 14/2;

y = 7.

Knowing y, we find x:

x = y + 6 = 7 + 6 = 13.

Find the area S of a given rectangle as the product of the length and width of a given rectangle:

S = 13 * 7 = 91.

Answer: The area of ​​this rectangle is 91.