Middle School

The length and width of a rectangle are consecutive even integers. The area of the rectangle is 120 square units. What are the length and width of the rectangle?

Answer :

The length and width of the rectangle is 12 and 10 respectively.

Let the consecutive integers be :

  • a ; a+2

Area of rectangle = Length × width

120 = a(a + 2)

120 = a² + 2a

a² + 2a - 120 = 0

a² - 10a + 12a + 120 = 0

a(a - 10) + 12(a - 10)

a = 10 or a = -12

The width cannot be negative, Hence, width = 10

Length = a + 2

Length = 10 + 2

Length = 12

The length and width of the rectangle is 12 and 10 respectively.