Question

The length and width of a rectangle are consecutive even integers. The area of the rectangle is 80 square units. What are the length and width of the rectangle?

Answer 1

10 and 8

Explanation:

consecutive even numbers have a difference of 2 between them.

let the width be n then the length is n + 2

Area = n(n + 2) = 80, thus

n² + 2n = 80 ( subtract 80 from both sides )

n² + 2n - 80 = 0 ← in standard form

(n + 10)(n - 8) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 10 = 0 ⇒ n = - 10

n - 8 = 0 ⇒ n = 8

But n > 0 ⇒ n = 8

width = n = 8 and length = n + 2 = 8 + 2 = 10