Question

A rectangle of perimeter 74 cm is 7cm longer than it is wide. what is the length of each side?​

Answer 1

I assume that you mean: the length is 7cm more than the width, and the perimeter is 74 cm.

If so, we can write down the following system, where l and w represent, respectively, the length and the width:

$\begin{cases}l=w+7\\2(l+w)=74\end{cases} \iff \begin{cases}l=w+7\\l+w=37\end{cases} \iff \begin{cases}l=w+7\\(w+7)+w=37\end{cases}$

We can easily solve the second equation:

$(w+7)+w=37 \iff 2w+7=37 \iff 2w=30 \iff w=15$

And finally solve for the length:

$l=w+7=15+7=22$