Question

kurt enlarges a 24 cm by 30 cm photo to a 60 cm by 75 cm photo. what is the scale factor of the enlargement?
3.125
2.5
2
0.4

Explanation:

Step1: Recall scale factor formula

The scale factor \( k \) is the ratio of the new length to the original length. For a rectangle, we can use either side (length or width) to calculate the scale factor since it's a uniform enlargement. Let's take the first dimension: original length \( l_1 = 24 \) cm, new length \( l_2 = 60 \) cm. The formula for scale factor is \( k=\frac{l_2}{l_1} \).

Step2: Calculate using width (optional check)

We can also check with the width: original width \( w_1 = 30 \) cm, new width \( w_2 = 75 \) cm. Then \( k = \frac{w_2}{w_1}=\frac{75}{30} = 2.5 \). Let's verify with length: \( \frac{60}{24}=\frac{5}{2}=2.5 \). So both give the same scale factor.

Answer:

2.5 (corresponding to the option "2.5")