Question

the triangle PRS and PQR are similar PS=2 and PR=3 if the area of triangle PRS is 2 cm sq. calculate the area of triangle PQR

Answer 1

Answer:

Given ;

∆ PRS ~ ∆ PQR

PS = 2 cm .

PR = 3 cm .

ar ( ∆ PRS ) = 2 cm² .

Find : ar (∆ PQR ).

Solution :

According to theorem 1 of similar triangles .

The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides .

So, from that ;

ar (∆ PRS ) / ar(∆ PQR ) = PS / PR

=> 2 / ar (∆ PQR ) = 2/3

=> ar ( ∆ PQR ) = 2/3 × 2 ( 2 and 2 get cancelled).

=> ar (∆ PQR ) = 3 cm².

Hence , the area of ∆ PQR = 3 cm² ( ans )...