Question 621041
You know that the surface area must be {{{60 ft^2}}}. You also know that length times width equals the area, A. Thus you can say that {{{L*W=60}}}, but you can also substitute in an alternate value for W since you know that width is 4 less than the length. Thus, we can now say {{{L*(L-4)=60}}} this is the same as saying {{{L^2-4L=60}}} (this was achieved by factoring). Now you can also say {{{L^2-4L-60=0}}}. We can now factor this expression and can determine that {{{(L-10)*(L+6)=0}}}. This means that either {{{L-10=0}}} or that {{{L+6=0}}}. If we solve for L-10=0 you get L=10; however if you solve for L+6=0 you get L=-6. Since you cannot have a negative length value the length must be 10 feet. Thus we can determine that the width must be 6 feet as {{{10-4=6}}}. Now, let's double-check to make sure that our length and width values result in a surface area of {{{60 ft^2}}}:
{{{10*6=60}}}
{{{60=60}}}
It works :)