Question

The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is the area of the original rectangle?

Answer 1

width = 6

length = 8

Explanation:

L = W + 2 : consecutive integers and length is larger than width

L * (W - 3) = 24 : area when width is decreased by 3 = 24

(W + 2) * (W - 3) = 24 : substitute W+2 for L in second equation

W^2 - W - 6 = 24 : multiplied

W^2 - W - 30 = 0 : subtracted 24 from both sides of equatin

(W - 6) * (W + 5) = 0 : factored. could use quadratic equation

W = 6 OR W = -5

W must be 6 as width must be positive

L is 8 as it is 2 more than W