Question

in the diagram below, (overline{qr}) is parallel to (overline{no}). (pr = 8.6), (qn = 8.6), and (ro = 6.4). find the length of (pq). round your answer to the nearest tenth if necessary.

Explanation:

Step1: Identify the theorem

Since \( QR \parallel NO \), by the Basic Proportionality Theorem (Thales' theorem), we have \(\frac{PQ}{QN}=\frac{PR}{RO}\).

Step2: Substitute the known values

We know that \( PR = 8.6 \), \( QN = 8.6 \), and \( RO = 6.4 \). Let \( PQ=x \). Then the equation becomes \(\frac{x}{8.6}=\frac{8.6}{6.4}\).

Step3: Solve for \( x \)

Cross - multiply to get \( x=\frac{8.6\times8.6}{6.4} \). First, calculate \( 8.6\times8.6 = 73.96 \). Then, divide by \( 6.4 \): \( x=\frac{73.96}{6.4}\approx11.55625 \). Rounding to the nearest tenth, we get \( x\approx11.6 \).

Answer:

\( 11.6 \)