jmc

If the perimeter of the room is 48 feet, then the semiperimeter is half that or 24 feet. This is the sum of the length and the width. The part-to-part ratio $5:3$ is a total of 8 parts, so each part must be worth $24÷8=3$ feet. That means the length is $5\times 3=15$ feet and the width is $3\times 3=9$ feet, so the area must be $15\times 9=\boxed{135\text{ square feet}}$.