Question

9 a flagpole casts a shadow 10 ft long. if a man 6 ft tall casts a shadow 4 ft long at the same time of day, how tall is the flagpole? 10 a photograph is 25 cm wide and 20 cm high. it must be reduced to fit a space that is 8 cm high. find the width of the reduced photograph.

Explanation:

Problem 9

Step1: Set up proportion

Let \( h \) be the height of the flagpole. The ratio of height to shadow length should be equal for the man and the flagpole. So, \(\frac{h}{10}=\frac{6}{4}\)

Step2: Solve for \( h \)

Cross - multiply: \( 4h = 6\times10 \)
\( 4h=60 \)
Divide both sides by 4: \( h=\frac{60}{4}=15 \)

Step1: Set up proportion

Let \( w \) be the width of the reduced photograph. The ratio of width to height should be the same for the original and reduced photograph. So, \(\frac{w}{8}=\frac{25}{20}\)

Step2: Solve for \( w \)

Cross - multiply: \( 20w = 25\times8 \)
\( 20w = 200 \)
Divide both sides by 20: \( w=\frac{200}{20}=10 \)

Answer:

The flagpole is 15 feet tall.

Problem 10