Question

a 30 - foot tall house casts a shadow that is 25 feet long. at the same time, a nearby apartment building casts a shadow that is 125 feet long. how tall is the apartment building to the nearest foot? the apartment building is approximately (square) feet tall.

Explanation:

Step1: Identify the ratio

Let the height of the house be \( h_1 = 30 \) feet, its shadow length \( s_1 = 25 \) feet. Let the height of the apartment building be \( h_2 \) and its shadow length \( s_2 = 125 \) feet. Since the ratio of height to shadow length is the same (similar triangles), we have \( \frac{h_1}{s_1}=\frac{h_2}{s_2} \).

Step2: Substitute values

Substitute \( h_1 = 30 \), \( s_1 = 25 \), \( s_2 = 125 \) into the equation: \( \frac{30}{25}=\frac{h_2}{125} \).

Step3: Solve for \( h_2 \)

Cross - multiply: \( 25h_2=30\times125 \). Then \( h_2=\frac{30\times125}{25} \). Simplify \( \frac{30\times125}{25}=30\times5 = 150 \).

Answer:

150