Question

use the diagram below to answer questions 24 - 25.

1. which proportion could find x, the distance across griffin lake?

a. $\frac{64}{84}=\frac{x}{92}$ c. $\frac{64}{92}=\frac{84}{x}$
b. $\frac{x}{64}=\frac{84}{92}$ d. $\frac{84}{x}=\frac{92}{64}$

1. find x.

Explanation:

Step1: Use the property of similar triangles

Since the two right - angled triangles are similar (by AA similarity, as the right angles are equal and the common angle is equal), the ratios of their corresponding sides are equal.
The ratio of the shorter legs to the longer legs of the two similar triangles gives the proportion.
The shorter legs are \(64\) and \(x\), and the longer legs are \(84\) and \(92\). So, \(\frac{64}{84}=\frac{x}{92}\)

Step2: Solve for \(x\) in the proportion \(\frac{64}{84}=\frac{x}{92}\)

Cross - multiply: \(84x = 64\times92\)
\(84x=5888\)
\(x=\frac{5888}{84}\approx70.1\)

Answer:

1. A. \(\frac{64}{84}=\frac{x}{92}\)
2. \(x\approx70.1\)