# The perimeter of the rectangle is 120 cm. The length of the rectangle is 10 cm longer than the width. Find the area.

Since we know the perimeter of the rectangle, let’s recall the formula by which it is found.

It is known that the perimeter of a rectangle is the sum of the lengths of all its sides.

According to the properties, the opposite sides of the rectangle are equal in pairs.

Then the formula for finding the perimeter can be written as P = 2 (a + b), where a and b are the lengths of the sides of the rectangle.

Let’s introduce a variable. Let’s denote the width of the rectangle as x cm, then the length will be equal to – (x + 10) cm.

Let’s create an equation using the formula for finding the perimeter:

120 = 2 (x + x + 10);

We solve a linear equation with one variable:

2 (2x + 10) = 120;

2x + 10 = 60;

2x = 60 – 10;

2x = 50;

x = 25.

So the width of the rectangle is 25 cm, and the length is 25 cm + 10 cm = 35 cm.

Find the area of a rectangle

Let’s remember the formula for finding the area of a rectangle. The area of the rectangle is equal to the product of the length and the width.

S = a * b, where a is the length and b is the width.

Substitute the found values for the length and width of the rectangle into the formula and calculate:

S = 25 * 35 = 875 cm ^ 2.

Answer: 875 cm ^ 2 is the area of a rectangle.