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 to calculate the scale factor. Let's take the first side: original length \( l_1 = 24 \) cm, new length \( l_2 = 60 \) cm. The formula is \( k=\frac{l_2}{l_1} \).

Step2: Calculate using first side

Substitute the values: \( k = \frac{60}{24} \). Simplify this fraction: \( \frac{60\div12}{24\div12}=\frac{5}{2} = 2.5 \). We can also check with the other side: original length \( w_1 = 30 \) cm, new length \( w_2 = 75 \) cm. \( k=\frac{75}{30}=\frac{5}{2}=2.5 \). So the scale factor is consistent.

Answer:

2.5 (corresponding to the option "2.5")