Question

1. a cat casts a 32 - inch shadow at the same time that a nearby flower casts an 8 - inch shadow. if the flower is 3 inches tall, how tall is the cat?
2. a 5 - foot - tall fencepost casts a 7.25 - foot shadow at the same time that a nearby gazebo casts a 36.25 - foot shadow. how tall is the gazebo?
3. at the same time that an 11 - inch - tall weathervane casts a 16 - inch shadow, a nearby lightning rod casts a 28 - inch shadow. how tall is the lightning rod?

Explanation:

Step1: Set up proportion

For problem 5: Let the height of the cat be \(x\). The proportion is \(\frac{x}{32}=\frac{3}{8}\).
For problem 6: Let the height of the gazebo be \(y\). The proportion is \(\frac{y}{36.25}=\frac{5}{7.25}\).
For problem 7: Let the height of the lightning rod be \(z\). The proportion is \(\frac{z}{28}=\frac{11}{16}\).

Step2: Solve proportion

For problem 5: Cross - multiply: \(8x = 3\times32\), \(8x=96\), \(x = 12\).
For problem 6: Cross - multiply: \(7.25y=5\times36.25\), \(7.25y = 181.25\), \(y=25\).
For problem 7: Cross - multiply: \(16z=11\times28\), \(16z = 308\), \(z=\frac{308}{16}=19.25\).

Answer:

1. The cat is 12 inches tall.
2. The gazebo is 25 feet tall.
3. The lightning rod is 19.25 inches tall.