Question

1. an obelisk casts a 27.5 - meter shadow at the same time that a nearby monument casts a 5.5 - meter shadow. if the monument is 4 meters tall, how tall is the obelisk?
2. at the same time that a 3.5 - foot - tall heron casts a 7.5 - foot shadow, a nearby reed casts a 32.25 - foot shadow. how tall is the reed?
3. a tree casts a 42 - foot shadow at the same time that a nearby flagpole casts a 12 - foot shadow. if the flagpole is 7.6 feet tall, how tall is the tree?

Explanation:

Step1: Set up proportion

Let the height of the obelisk be \(x\). The proportion is \(\frac{x}{27.5}=\frac{4}{5.5}\)

Step2: Cross - multiply

\(5.5x = 27.5\times4\)

Step3: Solve for \(x\)

\(x=\frac{27.5\times4}{5.5}\)
\(x = 20\)

Step1: Set up proportion

Let the height of the reed be \(y\). The proportion is \(\frac{y}{32.25}=\frac{3.5}{7.5}\)

Step2: Cross - multiply

\(7.5y=32.25\times3.5\)

Step3: Solve for \(y\)

\(y = \frac{32.25\times3.5}{7.5}\)
\(y=15.05\)

Step1: Set up proportion

Let the height of the tree be \(z\). The proportion is \(\frac{z}{42}=\frac{7.6}{12}\)

Step2: Cross - multiply

\(12z=42\times7.6\)

Step3: Solve for \(z\)

\(z=\frac{42\times7.6}{12}\)
\(z = 26.6\)

Answer:

20 meters