Question

the area of a rectangular wall of a barn is 36 square feet. Its length is 6 feet longer than twice its width. Find the length and width of the wall of the barn.

Answer 1

The length is 12 feet and width is 3 feet of the wall of the barn.

Explanation:

Given : The area of a rectangular wall of a barn is 36 square feet. Its length is 6 feet longer than twice its width.

To Find : The length and width of the wall of the barn ?

Solution :

Let the width of the wall is 'w'.

Its length is 6 feet longer than twice its width.

The length of the wall is l=6+2w

The area of the wall is 36 square feet.

The area of the rectangular wall is
`A=l* w`

`36=(6+2w)* w`

`36=6w+2w^2`

`w^2+3w-18=0`

Apply middle term split,

`w^2+6w-3w-18=0`

`w(w+6)-3(w+6)=0`

`(w+6)(w-3)=0`

`w=-6,3`

Reject w=-6

The width of the wall is w=3 feet.

The length of the wall is l=6+2(3)=6+6=12

Therefore, The length is 12 feet and width is 3 feet of the wall of the barn.

Answer 2

(6+2w)*w=36
6w+2w^2=36
2w^2+6w-36=0
2(w^2+3w-18)=0
2(w+6)(w-3)=0
w=3 or w=-6

width cannot be negative thus it must be 3 if the width is 3 then
36=3l
36/3=l
12=l

Hope this helps