WORD PROBLEM: Solve the word problem.

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

Assume the wall to be a rectangle with sides L and W. You are given two facts.

a) Area of the wall is 84 sq ft

i.e. L * W =84

b) width is 5ft longer than the length.

i.e. W = L + 5

Using substitution yields a quadratic equation.

e.g. L2 + 5L - 84 = 0

A quadratic equation generally has two solutions. This equation also has two (if you have difficulty finding the roots, lsend me a comment) has only one positive solution. The other is a negative value, and is physically meaningless.

The result is therefore,

L = 7 Ft

and W = 12 Ft.

Answer 2

Hello Lucy!

Let's call the Length "L".

If the width of the wallpaper is 5 feet more than the length, the the width is L+5

The area is the width multiplied by the length.

L*(L+5) = 84

L² + 5L - 84 = 0

By solving this equation we find the values for L as 7 and -12. Since L can only be positive, then:

Length = 7 and Width = 12