Question

use similar triangles and a proportion to find the length of the lake shown in the figure.
ft
50.0 ft
210 ft 140 ft
p

Explanation:

Step1: Set up the proportion

Let the length of the lake be \(x\). Since the triangles are similar, \(\frac{x}{50}=\frac{210 + 140}{140}\).

Step2: Simplify the right - hand side

\(\frac{210+140}{140}=\frac{350}{140}=\frac{5}{2}\). So the equation becomes \(\frac{x}{50}=\frac{5}{2}\).

Step3: Solve for \(x\)

Cross - multiply: \(2x=50\times5\). Then \(2x = 250\), and \(x=\frac{250}{2}=125\).

Answer:

\(125\)