Question

The area of a door is 3024 square inches. If

the length of the door is 48 inches longer
than the width of the door, what is the
width of the door?
A: Translate the problem into an equation.
B: Solve

Answer 1

Lets take all factors into consideration first

The door is a rectangle and the area of a rectangle is length times width

Let the width be w

Let the length be l

Equation length × breadth = area

(w+48)w = 3024

w^2 + 48w = 3024

w^2 + 48w - 3024 = 0

w^2 + 84w - 36w - 3024 = 0

w(w + 84) -36 ( w + 84) = 0

(w + 84) (w - 36) = 0

w + 84 = 0 AND w - 36 =0

w = -84 and w = 36

Since width cannot be negative, the right answer is 36

How did I get 84 and 36? Well, I had to factorize 3024 and since 84 times 36 is 3024 and 84 minus 36 is 48, I chose them.