Question

use similar triangles and a proportion to find the length of the lake shown here.
(hint: the side 76 m long in the smaller triangle corresponds to side of 76 m + 96 m = 172 m in the larger triangle.)
n = □ m

Explanation:

Step1: Set up the proportion

Since the triangles are similar, the ratios of corresponding sides are equal. We have the proportion \(\frac{76}{172}=\frac{38}{n}\).

Step2: Cross - multiply

Cross - multiplying gives us \(76n = 172\times38\).

Step3: Solve for \(n\)

First, calculate \(172\times38=(170 + 2)\times38=170\times38+2\times38=6460+76 = 6536\). Then, \(n=\frac{6536}{76}\).
Since \(6536\div76 = 86\).

Answer:

\(n = 86\)