In Fig. 4.177, . If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area () : area ().

Question

In Fig. 4.177, . If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area ( ) : area ( ).

Philoid · Accepted Answer

We have,

ΔACB ~ ΔAPQ

Then, AC/AP = CB/PQ = AB/AQ[Corresponding parts of similar Δ are proportional]

Or, AC/2.8 = 10/5 = 6.5/AQ

Or, AC/2.8 = 10/5 and 10/5 = 6.5/AQ

Or, AC = 5.6cm and AQ = 3.25cm

By area of similar triangle theorem

Area of ΔACB/Area of ΔAPQ = BC² /PQ²

= (10)²/(5)²

= 100/25

= 4 cm