Question

A rectangle's length is 4 feet more than its width. If the area of the rectangle is 396 square feet, what is its width, in feet?

Answer 1

W = x
L = x + 4

A = W * L
= x * (x + 4)
= x^2 + 4x

A also equals 396, so:
x^2 + 4x = 396

We need to factor:
x^2 + 4x - 396 = 0
Ax^2 + Bx + C
A = 1
B = 4
C = 396

Factors of A*C = 1*396 = 396:
https://www.easycalculation.com/factors-of-396.html

The factor pair 18*22 is what we want because:
22 - 18 = 4 = B

x^2 + 4x - 396 = 0
x^2 + 22x - 18x - 396 = 0
x(x + 22) - 18(x + 22) = 0
(x - 18)*(x + 22) = 0

When two numbers multiplied equals zero, at least one of them is zero. What happens when we try to make (x - 18) equal to zero:
x - 18 = 0
x = 18

When we try to make (x + 22) equal to zero:
x + 22 = 0
x = -22

Well, our width shouldn't be less than zero, should it? Let's rule out using the negative answer, because that wouldn't make much sense. That leaves x = 18 to be our width.

Width is 18 feet.

Answer 2

22 is the width because 18 multiplied by 22 is 396 and 22 is 4 more than 18.