Hi Colum,

Yes you can.

Let me do an example first. Suppose you know that the area is 80 square centimeters and the ratio of the length to the width is $5:4.$ Let the length be $l$ centimeters and the width $w$ centimeters. Since $l:w = 5:4$ you know that $4 \times l = 5 \times w$ or $l = \large \frac54 \normalsize \times w.$ Since $l \times w = 80$ square centimeters you have that

\[\frac54 w \times w = 80\]

or

\[w^2 = 80 \times \frac45 = 64\]

and hence $w = 8$ cm and $l = 10$ cm.

Thus in general if the rectangle dimensions are $l$ and $w$ units, the area is $A$ square units and $l:w = p:q$ then you know that $q \times l = p \times w.$ Solve this equation for $l,$ substitute into the area expression $A = l \times w$ and solve for $w.$

I hope this helps,
Penny