Question

In A ABC, PQ is a line segment intersecting AB at P and AC at Q
such that seg PQ || seg BC. If PQ divides A ABC into two equal parts
BP
having equal areas, find
BP/AB​

Answer 1

Answer:

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)

​

=

1

2

​

---- ( 1 )

Now, in △ABC and △APQ,

∠BAC=∠PAQ [ Common angles ]

∠ABC=∠APQ [ Corresponding angles ]

∴ △ABC∼△APQ [ By AA similarity ]

∴

area(△APQ)

area(△ABC)

​

=

AP

2

AB

2

​

∴

1

2

​

=

AP

2

AB

2

​

[ From ( 1 ) ]

⇒

AP

AB

​

=

1

2

​

​

⇒

AB

AB−BP

​

=

2

​

1

​

⇒ 1−

AB

BP

​

=

2

​

1

​

⇒

AB

BP

​

=1−

2

​

1

​

∴

AB

BP

​

=

2

​

2

​

−1

​