Question

The scale factor for two similar rectangles is 3. If the area of the smaller rectangle is 8 m2, what is the area

of the larger rectangle?
a. 24m²
b. 192m²
c. 72m²
d. 108m²

Answer 1

The area of the larger rectangle is 72 m² as the area scales by the square of the scale factor, which in this case is 9 (3 squared).

Step-by-step explanation:

If the scale factor for two similar rectangles is 3 and the area of the smaller rectangle is 8 m², to find the area of the larger rectangle, we need to apply the rule that the ratio of the areas of similar figures is equal to the square of the scale factor. In this case, we will square the scale factor, 3, to get 3², which equals 9. Therefore, the area of the larger rectangle is 9 times the area of the smaller rectangle.

To find the larger rectangle's area, multiply the area of the smaller rectangle by 9. So, 8 m² x 9 = 72 m². Hence, the answer is option c: 72 m².