Question

In the figure given below, if BD = 2.4 cm, AC = 3.6 cm, PD = 4 cm, PB = 3.2 cm, and AC is parallel to BD, then the lengths of PA & PC will be

• A. 4.8 cm and 6 cm respectively
• B. 6.8 cm and 4 cm respectively
• C. 6 cm and 4.8 cm respectively
• D. 4 cm and 6.8 cm respectively

Answer 1

The correct option is A

4.8 cm and 6 cm respectively

In $\Delta APC\&\Delta BPD$

$\angle APC=\angle BPD$ (Vertically opposite angle)
$\angle ACP=\angle BDP$ (Alternate angle)
$\therefore \Delta APC\sim \Delta BPD$ by AA similarity criterion.

$\frac{AP}{AC}=\frac{BP}{BD}$ (Ratio of corresponding sides of similar triangles)
$\frac{AP}{3.6}=\frac{3.2}{2.4}$
AP = 4.8 cm

Also, $\frac{PC}{AP}=\frac{PD}{BP}\frac{PC}{4.8}=\frac{4}{3.2}$
PC = 6 cm