If each room is a square, then,
area of living room = 12*12 = 144 square feet
area of dining room = 10*10 = 100 square feet
so the combined area would be 144+100 = 244 square feet
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Though it is more likely the rooms are rectangles that aren't squares.
If so, then,
area of living room = 12x square feet
area of dining room = 10y square feet
combined area = 12x+10y square feet
where x and y represent the lengths of the living room and dining room respectively.
Optionally, we can factor out the GCF 2 to get 12x+10y = 2(6x+5y)
So 12x+10y is equivalent to 2(6x+5y). They are two ways to represent the combined area.
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If we knew that y = x, then we could say the combined area is:
12x+10y = 12x+10x = (12+10)x = 22x square feet
Though this is just another assumption of course. You'll need to provide more information or ask your teacher about this problem. It seems like something is missing. If possible, please post a diagram. Thank you.
