Question

If the dimensions of a rectangle are increased by a scale factor of three, which of the following statements is true?

A. The area increases by a factor of 3.
B.The area increases by a factor of 9.
C.The perimeter increases by a factor of 6.
D.The perimeter increases by a factor of 2.

Answer 1

The area of the rectangle increases by a factor of 9.

Step-by-step explanation:

The correct answer is B. The area increases by a factor of 9.

When the dimensions of a rectangle are increased by a scale factor of three, both the length and the width of the rectangle are multiplied by 3.

Since the area of a rectangle is found by multiplying its length by its width, the new area of the rectangle would be (3 times the original length) multiplied by (3 times the original width), which simplifies to 9 times the original area.

Therefore, the area of the rectangle increases by a factor of 9.