Question

The area of a rectangular wall of a barn is 280280 square feet. its length is 88 feet longer than twice its width. find the length and width of the wall of the barn.

Answer 1

Hello,

Making an equation would be a good method to solve this problem.

The area of a rectangle is equal to $l * w$ , where l is the length and w is the width of the rectangle.

If the area of the wall is 280280, we know $l * w$ = 280280
We also know that the length is 88 feet longer than twice the width. Twice the width is equal to $2w$ , and the length is 88 feet longer than that, so $l = 2w + 88$.

So, we have a system of equations:
$l * w = 280280$
$l = 2w + 88$

Using the first equation, we can find the value of l and we get $l = \frac{280280}{w}$

We then plug in this value of l into the second equation, and we have:
$\frac{280280}{w} = 2w + 88$

Now, we can multiply by w on both sides, and subtract 280280 on both sides, and use the quadratic formula to get w ≈ 353, -397

The width of a wall cannot be negative, so the answer is 353 feet. 

To find l, and make sure of our answers, we should check it with the original problem to make sure it checks out.

Doing this, we get:
$353 * l = 280280$
Divide by 353 on both sides to get:
$l = 794$

Now, we should check it with the equation $l = 2w + 88$
794 = 2(353) + 88 
794 = 794, checks out.

So, the width of the wall of the barn is 353 feet, and the length of the wall of the barn is 794 feet.

Hope this helps! Feel free to contact me with any questions you may have.