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. 

135 feet²