Question

given triangle ABC similar to triangle PQR if AB/PQ=1/3 THEN find triangle ABC/PQR

Answer 1

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 is 1/9

Answer 2

AB and PQ are sides of two similar triangles which are the ratio 1 :3
then ABC/ PQR =(1/3)²
= 1/9