Call the length of a rectangular room is a

its width is b

We have:

\(\dfrac{a}{b}=\dfrac{5}{3}\Leftrightarrow\dfrac{a}{5}=\dfrac{b}{3}\)

Put \(\dfrac{a}{5}=\dfrac{b}{3}=k\left(k\in Z^+\right)\)

\(\Rightarrow\left\{{}\begin{matrix}a=5k\\b=3k\end{matrix}\right.\)

We also have:

( a + b ) x 2 = 48 (ft)

=> 5k + 3k = 24

=> 8k = 24

=> k = 3

\(\Rightarrow\left\{{}\begin{matrix}a=5.3=15\left(ft\right)\\b=3.3=9\left(ft\right)\end{matrix}\right.\)

So the room's area is: 15 x 9 = 135 (ft^2)

Lê Quốc Trần Anh selected this answer.