Question

1. in this figure, \\( \overline { p q } \parallel \overline { l n } \\).

what is the value of \\( x \\)?
a 3
b 4
c 6
d 5

Explanation:

Step1: Apply the basic proportionality theorem (Thales' theorem)

Since \(\overline{PQ}\parallel\overline{LN}\), we have \(\frac{MP}{PL}=\frac{MQ}{QN}\).

Step2: Substitute the given values

Given \(MP = 9\), \(PL=3\), \(MQ = 15\), and \(QN=x\). Then \(\frac{9}{3}=\frac{15}{x}\).

Step3: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(9x=3\times15\). So \(9x = 45\).

Step4: Divide both sides by 9

\(x=\frac{45}{9}=5\).

Answer:

C. 6