In adjacent fig P and Q are midpoint of AB and AC respectively BC=7x.Find PQ
Answers
Step-by-step explanation:
In the adjacent figure, P and Q are points on the sides AB and AC respectively of a triangle ABC. PQ is parallel to BC and divides the triangle ABC into 2 parts, equal in area. The ratio of PA:AB=
93391
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Medium
Solution
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Correct option is C)
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
Step-by-step explanation:
We have
(
AC
AQ
)=
9
3
=
3
1
(
AB
AP
)=
10.5
3.5
=
3
1
In ΔAPQ & ΔABC
(
AC
AQ
)=(
AB
AP
)
& ∠PAQ=∠BAC
Thus ΔAPQ∼ΔABC by SAS criterion.
Hence (
AC
AQ
)=(
BC
PQ
) (by cpst)
⇒
3
1
=(
BC
4.5
)
⇒BC=13.5cm.