Question

In the given figure, ∆ACB ∼ ∆APQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (∆ACB) : area (∆APQ).

Answer 1

Given: ΔACB is similar to ΔAPQ.

BC = 10 cm, PQ = 5cm, BA = 6.5cm and AP = 2.8 cm

TO FIND:

(1) CA and AQ

(2) Area of ΔACB : Area of ΔAPQ

(1) It is given that ΔACB $~$ ΔAPQ.

We know that for any two similar triangles the sides are proportional. Hence

$\frac{\mathrm{AB}}{\mathrm{AQ}}=\frac{\mathrm{BC}}{\mathrm{PQ}}=\frac{\mathrm{AC}}{\mathrm{AP}}$

Similarly,

(2) We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.

$\frac{\mathrm{ar}\left(∆\mathrm{ACQ}\right)}{\mathrm{ar}\left(∆\mathrm{APQ}\right)}={\left(\frac{\mathrm{BC}}{\mathrm{PQ}}\right)}^2={\left(\frac{10}{5}\right)}^2={\left(\frac{2}{1}\right)}^2=\frac{4}{1}$