Question

In figure, ∆ACB ~ ∆APQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm, AP = 2.8 cm, find CA and AQ.

In the following figure, ΔACB ~ ΔAPQ. If BC = 8 cm, PQ = 4 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ.

Answer 1

We have, ∆ACB ~ ∆APQ

`\Rightarrow \frac{AC}{AP}=\frac{CB}{PQ}=\frac{AB}{AQ} `

`\Rightarrow \frac{AC}{AP}=\frac{CB}{PQ}\text{ and }\frac{CB}{PQ}=\frac{AB}{AQ}`

`\Rightarrow \frac{AC}{2.8}=\frac{8}{4}\text{ and }\frac{8}{4}=\frac{6.5}{AQ} `

`\Rightarrow \frac{AC}{2.8}=2\text{ and }\frac{6.5}{AQ}=2`

AC = (2 × 2.8) cm = 5.6 cm and `AQ=\frac{6.5}{2}cm=3.25cm`