Question

P and Q are points on the sides AB and AC respectively of ∆ABC such that AP = 3.5 cm, PB = 7 cm, AQ = 3 cm and QC = 6 cm. If PQ = 4.5 cm, find BC.

Answer 1

Answer:

$\fbox{BC = 13.5}$

Step-by-step explanation:

$( \frac{aq}{ac}) = \frac{3}{9} = \frac{1}{2}$

$( \frac{ap}{ab}) = \frac{13.5}{10.5} = \frac{1}{3}$

===>In ∆APQ & ∆ABC

$( \frac{aq}{ac}) = (\frac{ap}{ab})$

===>&/_PAQ = /_BAC

===>∆APQ~∆ABC by (SAS) criteria

$hence( \frac{aq}{ac}) = ( \frac{pq}{bc})by \: (cpst) \\ = = > \frac{1}{3} = (\frac{4.5}{bc}) \\ bc \: = 13.5 \:$