Polynomial equations

Question

The length of a rectangular billboard sign is 4 feet shorter than twice the width. The signs area is 126. How do I set up an equation to solve for the length and width?

Answer 1

Let's solve this problem in two parts. First, let's determine the relationship between the length and width.The question gives us the length based on the width. So for any width, w, the length, l = 2w - 4.

Next we'll solve the area of the rectangle. Recall that the area of a rectangle can be expressed with the equation Area = length x width. We know that the Area => a = 126, length => l = 2w - 4, width => w.

126 = (2w - 4)(w)

126 = 2w² - 4w

63 = w² - 2w

0 = w² - 2w - 63

0 = (w - 9)(w + 7)

The zeros for this equation are w = 9 and w = -7. Since a length can't be negative, we know that w = 9. Now we check our work to confirm.

Area = Length x Width

A = (2w - 4) x (w)

A = (2(9) - 4) x (9)

A = (18 - 4) x 9

A = 14 x 9

A = 126