Question

Given triangle ABC ~ triangle PQR if AB/PQ=1/3 then find area of triangle ABC / triangle PQR

Answer 1

Solution :-

Given that the Δ ABC is similar to the 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 Δ ABC/Area of Δ PQR = (AB)²/(PQ)²

⇒ (1)²/(3)²

= 1/9

So, Area of triangle ABC/Area of triangle PQR is 1/9

Answer.

Answer 2

GIVEN:
ΔABC ~ Δ PQR & AB/PQ = 1/3
ar(ΔABC)/ar( Δ PQR )= AB²/ PQ²
[The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.]
ar(ΔABC)/ar( Δ PQR ) = 1²/3²
[Given =AB/PQ = ⅓]
ar(ΔABC)/ar( Δ PQR ) = 1/9
Hence, the Area of ΔABC/Area of ΔPQR = 1/9

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