# The area of a rectangular wall of a barn is 45 square feet. Its length is 12 feet longer than the...

## Question:

The area of a rectangular wall of a barn is 45 square feet. Its length is 12 feet longer than the width. Find the length and width of the wall of the barn.

## Rectangles

In geometry, a rectangle is a type of parallelogram, which is the general term for polygons with parallel and equal opposite sides, with four right interior angles.

The area of the rectangular barn would be given by

{eq}A=lw\\[0.2cm] 45=lw {/eq}

If the length of the rectangular barn is longer than the width by{eq}12\,\rm ft {/eq}, then we have

{eq}l=w+12 {/eq}

We can muliply l or w on both side of the equation above.

{eq}lw=w^2+12w\\[0.2cm] {/eq}

Then, we substitute the value of the area.

{eq}45=w^2+12w\\[0.2cm] w^2+12w-45=0\\[0.2cm] {/eq}

By factoring the quadratic equation, we can determine the value of the width.

{eq}(w+15)(w-3)=0\\[0.2cm] \text{Note: We only take the positive value.}\\[0.2cm] \mathbf{w=3\, \rm ft} {/eq}

On the other hand, the length would be given by

{eq}l=3+12\\[0.2cm] \mathbf{l=15\,\rm ft} {/eq}

Therefore, the length and width of the rectangular barn is 15 and 3 ft, respectively. 