# The sum of the length and width of the rectangle is 14 cm. The length is 4 cm greater than the width.

July 25, 2021 | education

| **The sum of the length and width of the rectangle is 14 cm. The length is 4 cm greater than the width. What is the area of this rectangle?**

a – the length of the rectangle

b – the width of the rectangle

Let’s compose a system of equations:

a + b = 14

a – b = 4

a + b = 14

a = 4 + b

4 + b + b = 14

a = 4 + b

2b = 10

a = 4 + b

b = 5 cm

a = 4 + 5 = 9 cm

From the system of equations, we found the length and width of the rectangle. Now we can calculate its area:

S = a * b = 5 * 9 = 45 sq. Cm.

Answer: the area of this rectangle is 45 square centimeters.