Question

a land surveyor must calculate the distance across a river, $overline{kl}$, in feet. the surveyor measures the distance of $overline{jk}$, $overline{kn}$, and $overline{lm}$. given that $overline{kn}$ is parallel to $overline{lm}$, what is the measure, in feet, of the distance across the river? 56 feet 77 feet 35 feet 48 feet

Explanation:

Step1: Identify similar triangles

Since $\overline{KN}\parallel\overline{LM}$, $\triangle{JKN}\sim\triangle{JLM}$ by the AA (angle - angle) similarity criterion (corresponding angles are equal because of parallel lines).

Step2: Set up proportion

The ratios of corresponding sides of similar triangles are equal. So, $\frac{JK}{JL}=\frac{KN}{LM}$. We know $JK = 21$ feet, $KN = 18$ feet, and $LM = 48$ feet. Let $JL=x$. Then $\frac{21}{x}=\frac{18}{48}$.

Step3: Cross - multiply and solve for $x$

Cross - multiplying gives us $18x=21\times48$. So, $x=\frac{21\times48}{18}=\frac{21\times8}{3}=56$ feet.

Answer:

56 feet