Question

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

Answer 1

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

HOPE THIS WILL HELP YOU….

Answer 2

Thank you for asking this question. Here is your answer:

We will use the theorem on similar triangles.

The area of the two triangles will be in a ratio of the squares of their corresponding sides.

Now we will let the unknown constant  of proportionality be x.

Now we will solve it:

Area of ΔABC/ Area of ΔPQR = AB²/PQ² ⇒ (1x)²/(3x)² ⇒ x²/9x²

Area of ΔABC : Area of ΔPQR = 1 : 9

So the final answer is 1:9

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