Question 122304
You have the correct equation set up


{{{x(x+3)=180}}} Start with the given equation




{{{x^2+3x=180}}} Distribute




{{{x^2+3x-180=0}}} Subtract 180 from both sides



{{{(x+15)(x-12)=0}}} Factor the left side. Note: if you need help with factoring , check out this <a href="http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/change-this-name4450.solver">solver</a>. 




Set each factor equal to zero



{{{x+15=0}}} or {{{x-12=0}}}



Now solve for x in each case


{{{x=-15}}} or {{{x=12}}}




Since a negative length/width doesn't make any sense, our only solution is 



{{{x=12}}}




So this means that the width is 12 yards. Now to find the length, simply add 3 yards to 12 to get {{{12+3=15}}}. So the length is 15 yards




Check:


Simply multiply the width 12 and the length 15 to get 



{{{12*15=180}}}


which is the area.


So this verifies our answer.