Question 125496
x is the width, x + 10 is the length.  The area is the length times the width or {{{x(x+10)}}} and is equal to 96 sq ft.


{{{x(x+10)=96}}}


{{{x^2+10x=96}}}


{{{x^2+10x-96=0}}}


Factors of -96 whose sum is +10 are -6 and +16, so:


{{{(x+16)(x-6)=0}}}, so {{{x=-16}}} or {{{x=6}}}.  You'll have a very hard time finding a barn wall with a width of -16 feet, so we can exclude that solution.  The width is 6 feet and the lenght is 6 + 10 or 16 feet.  That's a very tall, skinny barn or a long but very short barn.