We can start by finding the length of the current living room. We know that the area of the current living room is 108 square feet, and its width is 9 feet. We can use the formula for the area of a rectangle to find its length:
area = length x width
108 = length x 9
length = 108/9
length = 12 feet
So the current living room is 12 feet long.
Now, we can find the area of the addition by subtracting the area of the current living room from the total area of the remodeled living room:
area of addition = total area - current area
area of addition = 180 - 108
area of addition = 72 square feet
We can use the formula for the area of a rectangle to find the length of the addition:
area = length x width
72 = length x width
We know that the width of the addition is the same as the width of the current living room, which is 9 feet. So we can substitute 9 for the width and solve for the length:
72 = length x 9
length = 72/9
length = 8 feet
Therefore, the length of the addition is 8 feet.