Question

The area of a rectangular wall of a barn is 110110 square feet. its length is 1212 feet longer than twice its width. find the length and width of the wall of the barn.

Answer 1

A = l x w
l = 1212 + 2w 
110,110 = (1212 + 2w)w
$110,110 = 1212w + 2w^2$
$0=2w^2+1212w-110,110$
Use quadratic formula: $w = -1212+ \sqrt{1212^2-4(2)(-110,110)} =80.228$
You don't need the negative value of the quadratic formula since it's asking for area.
Plug in 80.228 into l = 1212 + 2w
l = 1212 + 2(80.228) = 1372.456
To double check, 1372.456 x 80.228 = 110,109.4 or about 110,110

So, width = 80.228 and length = 1372.456