# 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.

## Answer and Explanation:

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.**

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#### Learn more about this topic:

from Geometry: High School

Chapter 8 / Lesson 7