Question

answer each question and round your answer to the nearest whole number.

1. a 3 ft tall bird bath standing next to a tent casts a 4 ft shadow. if the tent is 6 ft tall, then how long is its shadow?
2. a 6 ft tall petrified stump standing next to an adult elephant casts a 12 ft shadow. if the adult elephant is 8 ft tall, then how long is its shadow?
3. a 10 ft tall adult elephant standing next to a tent casts a 6 ft shadow. if the tent is 5 ft tall, then how long is its shadow?
4. if a 3 ft tall lawn ornament casts a 1 ft long shadow, then how long is the shadow that a 9 ft tall tent casts?

Explanation:

Question 19

Step1: Set up proportion

Let \( x \) be the shadow length of the tent. The ratio of height to shadow length should be equal. So, \(\frac{3}{4}=\frac{6}{x}\)

Step2: Solve for \( x \)

Cross - multiply: \( 3x = 6\times4 \)
\( 3x=24 \)
Divide both sides by 3: \( x=\frac{24}{3}=8 \)

Step1: Set up proportion

Let \( y \) be the shadow length of the elephant. The ratio of height to shadow length is constant. So, \(\frac{6}{12}=\frac{8}{y}\)

Step2: Solve for \( y \)

Cross - multiply: \( 6y = 8\times12 \)
\( 6y = 96 \)
Divide both sides by 6: \( y=\frac{96}{6}=16 \)

Step1: Set up proportion

Let \( z \) be the shadow length of the tent. The ratio of elephant's height to its shadow length is equal to the ratio of tent's height to its shadow length. So, \(\frac{10}{6}=\frac{5}{z}\)

Step2: Solve for \( z \)

Cross - multiply: \( 10z=5\times6 \)
\( 10z = 30 \)
Divide both sides by 10: \( z = 3 \)

Answer:

The shadow length of the tent is 8 feet.

Question 20