Question

The floor plan of a factory is dilated by a factor of 4 to create a new, larger floor plan.

The area of the new floor plan is _______ times larger than the area of the original floor plan?

a. 4
b. 8
c. 16
d. 64
e. 256

Answer 1

The original floor could be rectangle in shape.

If we consider the length of floor to be 'L' and width of floor to be 'W',

then area of original floor = length x width = LW.

And if its dimensions are dilated by scale factor of 4 to make new floor, then new length and width would become four times of older values. So new length would be '4L' and new width would be '4W'

Now area of new floor = length x width = 4L x 4W = 16LW.

It is clear that the area of new floor is 16 times of the area of original floor.

So, option C i.e. 16 is the final answer.