Question

Give triangle ABC parallel to triangle PQR if AB / PQ is equal to 1 / 3 then find the area of triangle ABC / area of triangle PQR

Answer 1

Solution :-
Given that Δ ABC ~ Δ PQR
and, 
AB/PQ = 1/3
We know that the ratio of two similar triangles is equal to the ratio of the squares of their corresponding sides.
So, 
Area of triangle/Area of triangle PQR = (AB)²/(PQ)²
⇒ (1)²/(3)²
= 1/9
So, area of triangle ABC/area of triangle PQR is 1/9.
hope it may help u..
thanks.

Answer 2

Theorem :- when two triangles are similar , then ratio of area of triangles is directly proportional to square of their sides .
Mathematically , if ∆ABC~ ∆DEF
Then , ar(∆ABC)/ar(∆DEF) = AB²/DE² = BC²/EF² = CA²/FD²

Solution :- given ∆ABC ~ ∆PQR and AB/PQ = 1/3
∴ ar(∆ABC)/ar(PQR) = AB²/PQ² = [AB/PQ]² = 1/3² = 1/9

Hence, answer is19