Question

1. given the diagram below what is the length of (overline{rs}) or the distance across a body of water?

85 m
60 m
75 m
45 m

Explanation:

Step1: Identify similar triangles

The two right - angled triangles are similar. Let the length of \(\overline{RS}\) be \(x\). The ratio of corresponding sides of similar triangles is equal.

Step2: Set up the proportion

The ratio of the shorter sides is \(3:2\), and the ratio of the hypotenuses is \(x:50\). So, \(\frac{3}{2}=\frac{x}{50}\).

Step3: Solve for \(x\)

Cross - multiply: \(2x = 3\times50\), \(2x=150\), \(x = 75\).

Answer:

75 m