Question

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

Answer 1

For an instance, w represents the width, and (w + 2) represents the length.

Make an equation of area in terms of w
area = 120
l × w = 120
(w + 2) × w = 120

use distributive property to simplify
w² + 2w = 120

use completing square method to solve for w, add 1 to both side
w² + 2w + 1 = 120 + 1
w² + 2w + 1 = 121
(w + 1)² = 121
(w + 1)² = 11²
w + 1 = 11
w = 11 - 1
w = 10
The width is 10 units

Find the length
l = w + 2
l = 10 + 2
l = 12
The length is 12 units

ANSWER: 12 and 10 units

Answer 2

Let the integers be x and x+2
area of rectangle= length × breadth
x × (x+2) = 120
x square + 2x =120
x square + x = 60
x + x = root of 60
x = root of 60 / 2