The perimeter of the rectangle is 90 cm. The length is 3 and 1/2 times the width. Find the area of the rectangle

1. We will use the formulas:

a) the perimeter of the rectangle is equal to the doubled sum of its sides;

b) the area is equal to the product of length and width.

2. By the statement of the problem, it is known that the length is 3 1/2 times the width.

If we denote the width by x, then the length will be 3 1/2 x.

Let’s make the equation

x + 3 1/2 x = 90 cm;

4 1/2 x = 90 cm;

x = 90 cm: 9/2 = 20 cm.

Let’s calculate what the length value is

x * 3 1/2 = 20 cm * 7/2 = 140/2 cm = 70 cm.

3. Define the area S of the rectangle

S = 20 cm * 70 cm = 140 cm².

Answer: The area is 140 cm².