The scale factor for two similar rectangles is 9. If the area of the smaller rectangle is 3 cm^2, what is the area of the larger rectangle?
(1 point)
Responses
729 cm^2
243 cm^2
81 cm^2
27 cm^2
When dealing with similar figures, the scale factor for the area is the square of the scale factor for the lengths. In your question, if the scale factor for the lengths is 9, then the scale factor for the area will be 9^2 = 81.
If the area of the smaller rectangle is 3 cm^2, then to find the area of the larger rectangle, you multiply the area of the smaller one by the scale factor for the area:
Area of larger rectangle = Area of smaller rectangle × (Scale factor for area)
Area of larger rectangle = 3 cm^2 × 81
Area of larger rectangle = 243 cm^2
So, the correct answer is:
243 cm^2