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

Answer:

$L =21.945$ --- Length

$W = 7.9725$ --- Width

Step-by-step 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:

$W = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}$

This gives:

$W = \frac{-6 \± \sqrt{6^2 - 4*2*-175}}{2*2}$

$W = \frac{-6 \± \sqrt{1436}}{2*2}$

$W = \frac{-6 \± 37.89}{4}$

Split

$W = \frac{-6+ 37.89}{4}, W = \frac{-6- 37.89}{4}$

$W = \frac{31.89}{4}, W = \frac{-43.89}{4}$

The width cannot be negative;

So:

$W = \frac{31.89}{4}$

$W = 7.9725$

Recall that:

$L = 6 + 2W$

$L =6 + 2 * 7.9725$

$L =21.945$