Question

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

Select from the drop-down menu to correctly complete the statement.

The area of the new floor plan is [choose] times larger than the area of the original floor plan.

Answer 1

The area of the new floor plan is 16 times larger than the area of the original floor plan.

Explanation:

If the floor of the factory was dilated by a factor of 4

this means that it increased all sides by this factor.

As the area is proportional to the square of the length

A1 ∝ l²

The new Area A2, would be proportional to

A2 ∝ (4*l)² = 16*l²