Question

question
quadrilateral mnop is similar to quadrilateral qrst. find the measure of side st. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify corresponding sides

Since quadrilateral \( MNOP \sim QRST \), the ratio of corresponding sides is equal. Let \( OP = 8 \), \( NO = 17 \), \( SR = 58 \), and we need to find \( ST \). The corresponding sides are \( OP \) and \( ST \), \( NO \) and \( SR \)? Wait, no, let's check the order. \( MNOP \) and \( QRST \), so \( NO \) corresponds to \( SR \), and \( OP \) corresponds to \( ST \). So the ratio of similarity is \( \frac{SR}{NO}=\frac{58}{17} \), and then \( ST = OP\times\frac{SR}{NO} \).

Step2: Calculate the ratio

First, find the ratio of the corresponding sides. The side \( NO = 17 \) in \( MNOP \) corresponds to \( SR = 58 \) in \( QRST \). So the scale factor \( k=\frac{58}{17} \).

Step3: Find \( ST \)

The side \( OP = 8 \) in \( MNOP \) corresponds to \( ST \) in \( QRST \). So \( ST = OP\times k = 8\times\frac{58}{17} \).

Calculate \( 8\times58 = 464 \), then \( \frac{464}{17}\approx27.3 \) (rounded to the nearest tenth).

Answer:

\( 27.3 \)