Question

It is given that triangle ABC is similar to triangle PQR with BC/QR = 1/4, then ar(PRQ)/ar(ACB) =

Answer 1

Answer: 1/16

ok so we know that:

If the triangles are similar Then the ratio of the area of the triangle is equal to the square of the ratio of the corresponding sides, we can apply this proved equation by:

ar(PRQ)/ar(ACB) = BC²/QR²   so

ar(PRQ)/ar(ACB) = (1/4)²         so

ar(PRQ)/ar(ACB) = 1/16

∴ the result or answer is 1/16

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Answer 2

Given: triangle ABC is similar to triangle PQR

           BC/QR = 1/4

To find: ar(PRQ)/ar(ACB)

Solution: Given, triangle ABC ~ triangle PQR.

We know that for similar triangles, the ratio of area of triangle is equal to the ratio of square of corresponding sides.

(Area of ∆ABC)/(Area of ∆PQR) = (BC)²/(QR)²

⇒ (Area of ∆ABC)/(Area of ∆PQR) = (BC/QR)²

⇒ (Area of ∆ABC)/(Area of ∆PQR) = (1/4)²

⇒ (Area of ∆ABC)/(Area of ∆PQR) = 1/16

⇒ (Area of ∆PQR)/(Area of ∆ABC) = 16

Therefore, ar(PRQ)/ar(ACB) = 16.

Answer: 16