$\operatorname{lcm} (a,b)$ of rectangle's side lengths

Question

Knowing that the dimensions of a rectangle $ABCD$, $a$ and $b$ are proportional to $3$ and $5$ respectively and that their area is equal to $135~\text{cm}^2$, find the $\operatorname{lcm}(a, b)$.

(I already know the result, but I want to know how to do it step by step)

Answer 1

Knowing that the dimensions of a rectangle $ABCD$, $a$ and $b$ are proportional to $3$ and $5$ respectively and that their area is equal to $135~\text{cm}^2$, find the $\operatorname{lcm}(a, b)$.

Strategy:

1. Since the side lengths $a$ and $b$ are proportional to $3$ and $5$, respectively, let $a = 3x$ and $b = 5x$.
2. Since the area of rectangle $ABCD$ is equal to $135~\text{cm}^2$, $ab = (3x)(5x) = 135~\text{cm}^2$.
3. Solve for $x$ to determine $a$ and $b$.
4. Find $\operatorname{lcm}(a, b)$.

Judging by your answer in the comments, you did not take into account the fact that the side lengths are proportional to $3$ and $5$ and did not notice that the area of the rectangle you obtained with side lengths $3~\text{cm}$ and $5~\text{cm}$ does not have the required area of $135~\text{cm}^2$.