For this case we have that by definition, the area of a rectangle is given by:
[tex]A = w * l[/tex]
Where:
w: It is the width
l: It is the length
According to the problem data we have:
[tex]l = (w-10) \ ft\\A = 264 \ ft ^ 2[/tex]
So:
[tex]264 = w (w-10)\\264 = w ^ 2-10w\\w ^ 2-10w-264 = 0[/tex]
We solve. We look for two numbers that, when multiplied, result in -264 and when added, result in -10. These are:
-22 and 12
So:
[tex](w-22) (w + 12) = 0[/tex]
Thus, the solutions are:
[tex]w_ {1} = 22\\w_ {2} = - 12[/tex]
We choose the positive value. So the width of the corral is [tex]22 \ ft[/tex]
ANswer:
[tex]22 \ ft[/tex]
