Question

what is the value of x, given that (overline{pq}paralleloverline{bc})? 10 7 5 8 clear my selection

Explanation:

Step1: Use the basic proportionality theorem

Since \(\overline{PQ}\parallel\overline{BC}\), by the basic proportionality theorem (Thales' theorem), \(\frac{AP}{PB}=\frac{AQ}{QC}\). Here, \(AP = 7\), \(PB=14\), \(AQ=x\), and \(QC = 10\). So, \(\frac{7}{14}=\frac{x}{10}\).

Step2: Solve the proportion for \(x\)

Cross - multiply the proportion \(\frac{7}{14}=\frac{x}{10}\). We get \(14x=7\times10\). Then \(14x = 70\). Divide both sides by 14: \(x=\frac{70}{14}\).

Answer:

\(5\)