Question

In the following figure, ΔACB ~ ΔAPQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (ΔACB): area (ΔAPQ).

In the following figure, ΔACB ~ ΔAPQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (ΔACB): area (ΔAPQ).

Answer 1

We have,

ΔACB ~ ΔAPQ

Then,

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

`rArr"AC"/2.8=10/5=6.5/"AQ"`

`rArr"AC"/2.8=10/5` and `10/5=6.5/"AQ"`

`rArr"AC"=10/5xx2.8` and `"AQ"=6.5xx5/10`

⇒ AC = 5.6 cm and AQ = 3.25 cm

By area of similar triangle theorem

`("Area"(triangleACB))/("Area"(triangleAPQ))/"BC"^2/"PQ"^2`

`=10^2/5^2`

`=100/25`

= 4