Monica's rectangular living room is 12 ft by 15 ft she has a square rug that covers 5/9 of the area of the floor. what is the side length of the square rug?
The area of the living room = 12 * 15 = 180 square feet
The area of the rug is 5/9 of that, so
the area of the rug = 5/9 * 180 = 100 square feet
The rug is square, so
the area of the rug = (side length)^2
Since we just found out what the area of the rug is, put that value in for the area and solve for the side length.
100 square feet = (side length)^2
Take the + square root of both sides.
√100 = side length
10 feet = side length