Question

1. given the diagram below, find the height of the shorter tree. 16 m 10 m 12 m 14 m

Explanation:

Step1: Use the property of similar triangles

Since the two triangles are similar (by AA similarity, as the angles are equal), the ratios of their corresponding sides are equal. Let the height of the shorter tree be \( h \). We have the proportion \(\frac{h}{20}=\frac{15}{25}\).

Step2: Solve the proportion for \( h \)

Cross - multiply the proportion \(\frac{h}{20}=\frac{15}{25}\). We get \(25h = 15\times20\). Then \(25h=300\). Divide both sides by 25: \(h=\frac{300}{25}\).

Answer:

\(12\ m\)