Question

If P and Q are points on sides AB and AC of Triangle ABC Such that AP-3.5cm and PB=7 cm,AQ=3 cm and QC-6cm.lf PQ-4.5cm,then BC=?​

Answer 1

Given :  P and Q are points on sides AB and AC of Triangle ABC Such that AP-3.5cm and PB=7 cm, AQ=3 cm and QC-6cm.

PQ-4.5cm

To Find : BC=?​

Solution:

AP = 3.5 cm , PB = 7 cm

AB = AP + PB = 10.5 cm

AQ = 3 cm  QC = 6 cm

AC = AQ + QC = 3 + 6 = 9 cm

3.5/10.5  = 3/9  = 1/3

AP/AB = AQ/AC  and ∠A is common

Hence ΔAPQ ~ ΔABC as par SAS similarity

=> AP/AB = AQ/AC =  PQ/BC  = 1/3

=> 4.5/BC = 1/3

=> BC = 13.5  cm

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