in the given fig P and Q are points on the sides AB and AC respectively of a triangle ABC. PQ // BC and divides triangle ABC into two parts equal in area. Find the ratio of PA:PB
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Given that Area of the Δ APQ = Area of PQCB
That means Area Δ ABC = 2 Area of Δ APQ
Since PQ ∥ BC
Therefore, Δ APQ is similar to Δ ABC
We know that ratio of the areas of two triangles is equal to the square of ratio of their sides in case of similar triangles.
Therefore,
Areaof△ABC
Areaof△APQ
=
AB
2
PA
2
AB
2
PA
2
=
Areaof△ABC
Areaof△APQ
=
2
1
AB
PA
=
2
1
Therefore, PA:AB = 1:
2
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