The floor plan of a home is dilated by a factor of 8 to create a new, larger floor plan. the area of the new floor plan is (8, 16, 32, 64, 256) times larger than the area of the original floor plan?

Let 
x> Initial length x of the floor plan
y> Initial length y of the floor plan
A1> initial area of the floor plan
 1) A1= x*y

2) the floor plan of a home is dilated by a factor of 8
then
x2=8x
y2=8y

the new area A2=x2*y2
A2=(8x)*(8y)=64*x*y> 64*A1
A2=64*A1

the answer is 
The area of the new floor plan is 64 times larger than the area of the original floor plan

Wow. that is a really cool question.

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