In Fig. 7.178, $Δ A C B \sim Δ A P Q$ . If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area $(Δ A C B)$ : area $(Δ A P Q)$ .

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Solution

It is given that ΔACB∼ΔAPQ
then,
$fraction numerator B C over denominator P Q end fraction equals fraction numerator A C over denominator A P end fraction equals fraction numerator A B over denominator A Q end fraction$ ( Corresponding parts of similar triangles)
$10 over 5 equals fraction numerator A C over denominator 2.8 end fraction equals fraction numerator 6.5 over denominator A Q end fraction A C space equals 5.6 space c m A Q space equals space 3.25 space c m$

By property of similar triangle
$fraction numerator A r triangle A C B over denominator A r triangle A P Q end fraction equals left parenthesis fraction numerator B C over denominator Q P end fraction right parenthesis squared equals 2 squared equals 4$
area (ΔACB): area (ΔAPQ). is 4:1

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