Question

use similar triangles and a proportion to find the length of the lake shown here.
(hint: the side 82 m long in the smaller triangle corresponds to side of 82 m + 102 m = 184 m in the larger triangle.)
n = m

Explanation:

Step1: Set up proportion

Since the two triangles are similar, the ratios of their corresponding sides are equal. Let the height of the larger - triangle be $n$ and the height of the smaller triangle is 41 m. The ratio of the base of the smaller triangle (82 m) to the base of the larger triangle (184 m) is equal to the ratio of the height of the smaller triangle to the height of the larger triangle. So, $\frac{82}{184}=\frac{41}{n}$.

Step2: Cross - multiply

Cross - multiplying gives us $82n = 41\times184$.

Step3: Solve for $n$

First, calculate $41\times184 = 7544$. Then, $n=\frac{7544}{82}$. Since $7544\div82 = 92$, $n = 92$.

Answer:

92