Question

which shadow puppet set-up must have a scale factor of 3? *
which shadow puppet set-up must have a scale factor of 3?
a
2.5 ft
7.5 ft
b
7.5 ft
2.5 ft
c
2.5 ft
2.5 ft
d
7.5 ft
2.5 ft

Explanation:

Step1: Recall Scale Factor Definition

Scale factor is the ratio of corresponding lengths (image to object or vice versa). For shadow puppets, we compare the distance from light to shadow (\(d_{shadow}\)) and light to puppet (\(d_{puppet}\)) or heights. The scale factor \(k=\frac{d_{shadow}}{d_{puppet}}\) (or height ratio).

Step2: Analyze Option A

• Distance from light to puppet: \(2.5\) ft.
• Distance from light to shadow: \(7.5\) ft.
• Scale factor \(=\frac{7.5}{2.5}=3\). Let's check others to confirm.

Step3: Analyze Option B

• Distance from light to puppet: \(2.5\) ft.
• Distance from light to shadow: \(7.5\) ft? Wait, no—here the \(7.5\) ft is the puppet - to - shadow? No, the diagram shows the light - to - shadow arm is \(7.5\) ft? Wait, no, in B, the light is at the \(2.5\) ft mark, and the shadow is at \(7.5\) ft from... Wait, no, re - examining: In A, the light to puppet is \(2.5\), light to shadow is \(7.5\) (total distance from light to shadow is \(2.5 + 5\)? No, no—wait, the scale factor for similar triangles (light, puppet, shadow) is based on the ratio of the distances from the light. So if the puppet is \(2.5\) ft from light, and shadow is \(7.5\) ft from light, then scale factor (shadow size / puppet size) is \(\frac{7.5}{2.5}=3\). In B, the \(7.5\) ft is the length of the arm, not the distance from light to shadow. In C, both distances are \(2.5\), scale factor \(1\). In D, the shadow is \(7.5\) ft from puppet, not light—so ratio would be \(\frac{2.5 + 7.5}{2.5}=\frac{10}{2.5}=4\), not 3. So A has scale factor \(3\).

Answer:

A