Question

In the following figure, line PQ || side BC, AP = 1 2 AB. If A(Δ APQ) = 16, find A(Δ ABC

Answer 1

Given :- In the following figure, line PQ || side BC, AP = 1/2 AB. If A(ΔAPQ) = 16, find A(ΔABC) = ?

Solution :-

in ∆APQ and ∆ABC,

→ ∠APQ = ∠ABC (since PQ || BC, therefore, corresponding angles .)

→ ∠AQP = ∠ACB (Corresponding angles.)

→ ∠PAQ = ∠BAC (common.)

so,

→ ∆APQ ~ ∆ABC .

Now, we know that,

• If two triangles are similar, then the ratio of the area of both triangles is proportional to the square of the ratio of their corresponding sides.

given that,

→ AP = (1/2)AB

→ AP / AB = (1/2)

therefore,

→ A(∆APQ) / A(∆ABC) = (1/2)²

→ 16 / A(∆ABC) = 1/4

→ A(∆ABC) = 64 unit² . (Ans.)

Learn more :-

In ABC, AD is angle bisector,

angle BAC = 111 and AB+BD=AC find the value of angle ACB=?

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