The area of a rectangular wall

Question

The area of a rectangular wall of a barn is 168 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.

Answer 1

We know nothing about the width. THAT is where you assign the variable.

The width is W.

 

THe length is 10 feet longer than twice the width.

THe Length is L = 10 + 2W

 

Area = length x width

168 = (10 + 2W)*w

 

168 = 10W + 2w^2

 

2W^2 + 10W - 168 = 0

 

W^2 + 5W - 84 = 0

 

(W     + 12  )( W   -      7    ) = 0

 

W+12 = 0 or W-7 = 0

 

W = -12 or W = 7

 

The width cannot be negative

so the solution W = -12 is

disqualified and rejected.

 

So W = 7

 

The length is 2*7 + 10 = 14 + 10 = 24

 

The area is 24 x 7 = 168

 

Length is 24 , width is 7

 

Answer 2

Let x = width.  Then length = 2x+10.

 

So, x(2x+10) = 168

 

2x² + 10x - 168 = 0

 

x² + 5x - 84 = 0

 

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

 

x = -12 or x = 7

 

Since x is the width, x can't be negative.

 

So, x = 7 ft = width                      

 

Length = 2x+10 = 24 ft