Question

In∆ABC,PQ||BC.SegPQ divides into two equal parts of area find BP/AP​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

Since the line PQ divides △ABC into two equal parts,

area(△APQ)=area(△BPQC)

⇒ area(△APQ)=area(△ABC)−area(△APQ)

⇒ 2area(△APQ)=area(△ABC)

∴ area(△APQ)/area(△ABC) = 2/1..............(1)

Now, in △ABC and △APQ,

∠BAC=∠PAQ [ Common angles ]

∠ABC=∠APQ [ Corresponding angles ]

∴ △ABC∼△APQ [ By AA similarity ]

∴area(△ABC)/area(△APQ) =AB^2/AP^2

so from eq 1,

AB^2/AP^2 = 2/1

⇒ AB/AP=√2/1

⇒ AB-BP/AB =1/√2

⇒1- BP/AB = 1/√2

BP/AB =1-1/√2

∴ BP/ AB = √2-1/√2