1) In the adjacent figure length of line segment
A P B
AB is 15cm, if it is divided into 5 equal
parts then find AP : PB
Answers
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Step-by-step explanation:
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 their sides in case of similar triangles.
Therefore,
Areaof△ABC
Areaof△APQ
=
AB
2
PA
2
or,
AB
2
PA
2
=
Areaof△ABC
Areaof△APQ
=
2
1
or
AB
PA
=
2
1
Therefore, PA : AB = 1:
2
The ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides.
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