The area of a rectangle wall of a barn is 234 square feet. it's length is 8 feet longer than twice its width. find the length and width of the wall of the barn.

First:
Area=length•width

Now, we know that the area is 234 & the length is 8 feet longer than twice its width. So, if width is w:
234 = w(2w+8)
Now, simplify:
234=2w^2+8w
This is starting to look like a quadratic:
0=2w^2+8w-234
0=w^2+4w-117
Factor it out:
0=(w+13)(w-9)
So w=9, -13
Now, since we're dealing with the real world, we'll say w=9 (because you can't have negative distance).
So, our width is 9 feet.
234=9(18+8)
234=9(26)
And so the length is 26 feet:
26x9 feet

Hope this helps!