Question

Suppose the area of a rectangle is 63 cm^2. If the width is 2 cm more than the length, find the length and width of the rectangle.

x = length
x + 2 = width

We know that the area of a rectangle is equal to the product of the length and width.
(x)(x + 2) = 63
x^2 + 2x = 63
x^2 + 2x - 63 = 0

Now, factoring,.
(x - 7)(x + 9) = 0
x - 7 = 0 or x + 9 = 0
x = 7 or x = -9

We have two solutions -- 7 and - 9. How do we determine the length and width???

Answer 1

The lenght and/or width of a rectangle can't get a negative value, so the answer is 7 :)