In the adjoining figure, MN || QR. If PN = 3.6 cm, NR = 2.4 cm and PQ = 5 cm, then PM is

1. 4 cm

2. 3.6 cm

3. 2 cm

4. 3 cm

Given MN || QR.

Considering △PMN and △PQR,

∠P = ∠P (Common angles)
∠PMN = ∠PQR (Corresponding angles are equal)

Hence, by AA axiom △PMN ~ △PQR.

Let length of PM be x cm.

Since triangles are similar by basic proportionality theorem,

$\therefore \dfrac{PM}{MQ} = \dfrac{PN}{NR} \\[1em] \Rightarrow \dfrac{PM}{PQ - PM} = \dfrac{PN}{NR} \\[1em] \Rightarrow \dfrac{x}{5 - x} = \dfrac{3.6}{2.4} \\[1em] \Rightarrow \dfrac{x}{5 - x} = \dfrac{36}{24} \\[1em] \Rightarrow 24x = 36(5 - x) \\[1em] \Rightarrow 24x = 180 - 36x \\[1em] \Rightarrow 24x + 36x = 180 \\[1em] \Rightarrow 60x = 180 \\[1em] \Rightarrow x = 3.$

∴ Length of PM = 3 cm.

Hence, Option 4 is the correct option.