Question

The area of a rectangular wall of a barn is 175 square ft.it’s length is 6feet longer than twice its width.find the length and width of the wall barn.

Answer 1

`L =21.945` --- Length

`W = 7.9725` --- Width

Explanation:

Given

Let

`L \to Length`

`W \to Width`

So:

`Area = 175`

`L = 6 + 2W`

Required

The dimension of the rectangle

The area is calculated as:

`Area =L*W`

This gives:

`175 =L*W`

Substitute:
`L = 6 + 2W`

`175 =(6 + 2W)*W`

Open bracket

`175 =6W + 2W^2`

Rewrite as:

`2W^2+ 6W -175 = 0`

Using quadratic formula:

`W = (-b \± √(b^2 - 4ac))/(2a)`

This gives:

`W = (-6 \± √(6^2 - 4*2*-175))/(2*2)`

`W = (-6 \± √(1436))/(2*2)`

`W = (-6 \± 37.89)/(4)`

Split

`W = (-6+ 37.89)/(4), W = (-6- 37.89)/(4)`

`W = (31.89)/(4), W = (-43.89)/(4)`

The width cannot be negative;

So:

`W = (31.89)/(4)`

`W = 7.9725`

Recall that:

`L = 6 + 2W`

`L =6 + 2 * 7.9725`

`L =21.945`