Questions: Which proportion can be used to find the value of PR if triangle XMQ is similar to triangle PRS? (F) 14/20 = 15/PR (G) 15/20 = 14/PR (ㅂ) 20/15 = 14/PR (1) 10/5 = 7/PR

Transcript text: Which proportion can be used to find the value of $\overline{P R}$ if $\triangle X M Q$ is similar to $\triangle P R S$ ? (F) $\frac{14}{20}=\frac{15}{P R}$ (G) $\frac{15}{20}=\frac{14}{P R}$ (ㅂ) $\frac{20}{15}=\frac{14}{P R}$ (1) $\frac{10}{5}=\frac{7}{P R}$

Solution

Solution Steps

Step 1: Find the corresponding sides

The problem states that $\triangle XMQ$ is similar to $\triangle PRS$. Therefore, the corresponding sides are: XM and PR MQ and RS XQ and PS

Step 2: Set up the proportion

We are given the lengths of XM (14), XQ (16), and PS (15). We want to find the length of PR. We can set up a proportion using the corresponding sides:

$\frac{XM}{XQ} = \frac{PR}{PS}$

Step 3: Substitute the values and simplify

Substituting the given values, we get:

$\frac{14}{16} = \frac{PR}{15}$

Simplifying the fraction 14/16, we get 7/8.