The area of a rectangular wall of a barn is 126 square feet. Its length is 4 feet longer than twice its width. Find the length and width of the wall of the barn

Question

The area of a rectangular wall of a barn is 126 square feet. Its length is 4 feet longer than twice its width. Find the length and width of the wall of the barn

Answer 1

Hello Deshun

 

We have a rectangle with an area of 126

 

Area = LW = 126

L = length

W = width

 

The second sentence tells us

L = 2W + 4

 

We can use substitution

LW = 126

(2W+4)W = 126

2W² + 4W = 126

 

and

2W² + 4W - 126 = 0

 

Since all the coefficients are even, we can divide by 2

W² + 2W - 63 = 0

 

We can factor this expression

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

 

Setting each factor equal to 0

(W+9) = 0

(W-7) = 0

 

And solving each for W,

W = -9

W = 7

 

But we can through out the W=-9 since a measurement cannot be negative. 

 

So, W=7

L = 2W + 4 = 2(7) + 4 = 14+4=18

 

Length = 18

Width = 7