Question

original |how do the areas compare?| scaled
15 cm
8 cm
a = 120 cm²
45 cm
24 cm
a = 1,080 cm²
the scaled rectangles area is 3 times larger than the original rectangles area.
the scaled rectangles area is 9 times larger than the original rectangles area.

Explanation:

Step1: Identify scale - factor of length

The length of the original rectangle is 15 cm and of the scaled - rectangle is 45 cm. The scale - factor of length $k=\frac{45}{15}=3$.

Step2: Recall area - scale relationship

For similar figures, if the scale - factor of length is $k$, the scale - factor of area is $k^{2}$. Since $k = 3$, the scale - factor of area is $k^{2}=3^{2}=9$.

Answer:

The scaled rectangle's area is 9 times larger than the original rectangle's area.