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

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.