length and width

Question

The area of a rectangular wall of a barn is 133 square feet. Its length is 12 feet longer than the width. Find the length and the width of the wall.

Answer 1

Hello Kay,

 

Start off with what you know:

Area of the barn= 133 sq ft.

The formula for the area of a rectangle = LW= length* width

 

If the length is 12 feet LONGER than the width:

L= 12 + W

 

Rearrange your original formula for the area:

Area=(12+W)W

 

Solve:

133= 12W + W²

 

Use your quadratic formula:

W² + 12W - 133

 

You should get 7 and -19 (you can never have a negative length), so the width should be 7

Length= 7 + W= 7 + 12= 19

 

I hope this helps! 

Answer 2

Area of a Rectangle = Length x Width
We can set width = w
Since length is 12ft longer than the width, we can express it as:
length = (w+12)

Substitute these into our Area equation, we see that:
133=(w+12) x w
We can then distribute the w outside of the parenthesis to each unit on the inside:
133=w²+12w

This can be rewritten into a quadratic formula (ax2+bx+c=0) and then factored:
w²+12w-133=0
(w+19)(w-7)=0
Which tells us w = -19, or +7
However, because a width cannot be negative, we discard w=-19
So width = 7 feet

To find the length, substitute w=7 into our original length equation
length = w+12
length = 7+12
length = 19ft

Solution:
length=19ft
width=7ft