Question

1. a 2-meter street sign casts a 0.3-meter shadow. at the same time, an 8.2 meter telephone pole casts a shadow. how long is the telephone pole’s shadow?
2. a child 4 ½ feet tall casts a 6-ft shadow. a nearby statue casts a 15-ft shadow. what is the height of the statue?

Explanation:

Problem 9:

Step1: Set up proportion

Let \( x \) be the length of the telephone pole's shadow. The ratio of height to shadow length should be equal. So, \(\frac{2}{0.3}=\frac{8.2}{x}\)

Step2: Cross - multiply and solve

Cross - multiplying gives \( 2x = 0.3\times8.2 \). Then \( 2x=2.46 \), and dividing both sides by 2, we get \( x=\frac{2.46}{2} = 1.23 \)

Step1: Set up proportion

Let \( h \) be the height of the statue. The ratio of the child's height to shadow length is equal to the ratio of the statue's height to its shadow length. So, \(\frac{4\frac{1}{2}}{6}=\frac{h}{15}\)

Step2: Convert mixed number and solve

First, \( 4\frac{1}{2}=\frac{9}{2} \). Cross - multiplying gives \( 6h=\frac{9}{2}\times15 \). \( 6h=\frac{135}{2} \), then \( h=\frac{135}{2\times6}=\frac{135}{12} = 11.25 \)

Answer:

The length of the telephone pole's shadow is \( 1.23 \) meters.

Problem 10: