Question

1. what would be the actual length, if the length of the model is 25 ft and the scale factor is lesser than one? a) 20 ft b) 25 ft c) 30 ft

Explanation:

Step1: Recall scale factor concept

A scale factor \( s \) (less than 1) means \( \text{Actual Length} = \text{Model Length} \times \frac{1}{s} \) (since \( s=\frac{\text{Model}}{\text{Actual}} \), so \( \text{Actual}=\frac{\text{Model}}{s} \)). If \( s < 1 \), then \( \frac{1}{s}>1 \), so actual length > model length.

Step2: Analyze options

Model length is 25 ft. Option a (20 ft) < 25, option b (25 ft) = 25, option c (30 ft) > 25. Only c satisfies actual length > model length when scale factor < 1.

Answer:

c) 30 ft