Question
In the given figure, $\triangle\text{ACB}\sim\triangle\text{APQ}.$ If BC = 8cm, PQ = 4cm, BA = 6.5cm and AP = 2.8cm, find CA and AQ.
✓
Answer
It is given that $\triangle\text{ACB}\sim\triangle\text{APQ}$
BC = 8cm, PQ = 4cm, BA = 6.5cm and AP = 2.8cm.
We have to find CA and AQ
Since $\triangle\text{ACB}\sim\triangle\text{APQ}$
$\Rightarrow\frac{\text{BA}}{\text{AQ}}=\frac{\text{CA}}{\text{AP}}=\frac{\text{BC}}{\text{PQ}}$
So $\frac{6.5\text{cm}}{\text{AQ}}=\frac{8\text{cm}}{4\text{cm}}$
$\text{AQ}=\frac{6.5\text{cm}\times4\text{cm}}{8\text{cm}}$
$=3.25\text{cm}$
Similarly $\frac{\text{CA}}{\text{AP}}=\frac{\text{BC}}{\text{PQ}}$
$\frac{\text{CA}}{2.8\text{cm}}=\frac{8\text{cm}}{4\text{cm}}$
$\text{CA}=2.8\text{cm}\times2\text{cm}$
$=5.6\text{cm}$
Hence, CA = 5cm and AQ = 3.25cm.
BC = 8cm, PQ = 4cm, BA = 6.5cm and AP = 2.8cm.
We have to find CA and AQ
Since $\triangle\text{ACB}\sim\triangle\text{APQ}$
$\Rightarrow\frac{\text{BA}}{\text{AQ}}=\frac{\text{CA}}{\text{AP}}=\frac{\text{BC}}{\text{PQ}}$
So $\frac{6.5\text{cm}}{\text{AQ}}=\frac{8\text{cm}}{4\text{cm}}$
$\text{AQ}=\frac{6.5\text{cm}\times4\text{cm}}{8\text{cm}}$
$=3.25\text{cm}$
Similarly $\frac{\text{CA}}{\text{AP}}=\frac{\text{BC}}{\text{PQ}}$
$\frac{\text{CA}}{2.8\text{cm}}=\frac{8\text{cm}}{4\text{cm}}$
$\text{CA}=2.8\text{cm}\times2\text{cm}$
$=5.6\text{cm}$
Hence, CA = 5cm and AQ = 3.25cm.
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