3. The length of a rectangle is three times its width. If the length is decreased by 5 and the width is increased by 5 , the rectangle becomes a square. Determine the length of the original rectangle.
3. Let the length of the original rectangle be $l$ and the width of the original rectangle be $w$.
Since the length is three times the width, then $l=3 w$.
We are also told that if the length is decreased by 5 and the width is increased by 5 , then the rectangle becomes square. This means that $l-5=w+5$.
Substituting the first equation into the second, we obtain $3 w-5=w+5$ or $2 w=10$, from which $w=5$.
Since $l=3 w$, then $l=3(5)=15$; that is, the length of the original rectangle is 15 .
ANSWER: 15