Question 1166619
<br>
width: w
length: w+3
area: w(w+3)=130<br>
If a formal algebraic solution is required, then<br>
{{{w(w+3)=130}}}
{{{w^2+3w-130=0}}}
{{{(w-10)(w+13)=0}}}
{{{w=10}}} OR {{{w=-13}}}<br>
Reject the solution w=-13 because it makes no sense in the problem.<br>
ANSWER: width = w = 10; length = w+3 = 13.<br>
Note that to solve the problem using formal algebra, you had to factor that quadratic equation, which means finding two numbers whose difference is 3 and whose product is 130.<br>
But that's what the original problem asked you to do....  So the formal algebra didn't save you any work.<br>
So if formal algebra is not required, simply look at the area of 130 and see that it is 13 times 10; 13 is 3 more than 10, so you have the answer, and in only a few seconds.<br>