Question

In the adjoining figure, AP = 1 cm, BP = 2 cm, AQ = 1.5 cm, and AC = 4.5 cm.

Prove that ΔАPQ ~ ΔАВС. Hence, find the length of PQ if BC = 3.6 cm.

Answer 1

Given, AP = 1 cm, BP = 2 cm, AQ = 1.5 cm, AC = 4.5 cm

QC = AC – AQ

= 3 cm

In ΔAPQ and ΔABС

`(AP)/(AB) = 1/3, (AQ)/(AC) = 1.5/7.5 = 1/3`

∠PAQ = ∠BAC    ....(Common)

ΔАРО ∼ ΔАВС   ....(By S.A.S. similarity rule)

`(AP)/(AB) = (PQ)/(BC)`  ....(By Thale’s theorem)

`1/(AP + PB) = (PQ)/3.6` ....(AP = 1 cm and BC = 3.6 cm)

`1/(1 + 2) = (PQ)/3.6`

PQ = 1.2 cm