Word problem length width

Question

Steven needs to purchase enough wallpaper to cover a wall measuring 84 square feet. If the width is 5 feet more than the length.what are the dimensions of the wall?

Length

Width

Answer 1

In this problem you need to use the formula

Area = Length x width

Define the variables

Length = x

Width = x+5 (Since width is 5 more than the length)

Plugging into the equation

84=x(x+5)

Distributing the x

84=x^2+5x

Subtract 84 from both sides

84-84=x^2+5x-84

Result is

0=x^2+5x-84

You have to solve this. It can be factored

0=(x+12)(x-7)

Setting each factor equal to zero and solve:

x+12=0

x=-12 (cannot be the answer, dimensions of a room cannot be negative)

x-7=0

x=7

Length = 7 ft

Width = 7+5 = 12 ft

Checking: 12 x 7 = 84 sq ft.