The ratio of the length of a rectangular room to its width is $5:3$. the perimeter of the room is 48 feet. what is the area of the room?

We can let x be the common factor shared by the length and width. Since their ratio is 5:3, then multiplying their common factor, their values would be 5x and 3x.

Now, recall that perimeter is the distance around the rectangle. Mathematically, we have Perimeter = 2 (Length + Width). Since length is 5x and width is 3x, we have

2 (5x + 3x) = 48

5x + 3x = 24

8x = 24

x = 3

Since the value of x is 3, the length would be 5 (3) = 15 and width would be3 (3) = 9. Knowing this, the area would be 15 (9) = 135 feet².

Answer: 135 feet²