Question

in a triangle ABC p and q are points on sides AB and AC respectively such that PQ is parallel to BC if AP = 2.4 AQ =2 QC =3 and BC = 6. find AP and PQ​

Answer 1

Given:-

• In a ∆ ABC , p and q are points on sides AB and AC respectively.

• PQ is parallel to BC .

• AP = 2.4 AQ =2 QC =3 and BC = 6.

To find :-

• AP and PQ

Solution:-

According to Basic proportionality theorem :-

• If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.

.°. AQ / QC = AP/PB

=> 2/3 = 2.4/PB

=> PB = 3.6 .

Therefore,

=> AB = AP+PB =2.4 +3.6 = 6cm.

Given that PQ || BC ,

/_ AQP =/_ ACB

/_APQ = /_ABC

By AAA similarity ,

• ∆ AQP ~ ∆ ACB

Therefore ,

=> AQ / AC = QP / CB

=> 2/5 = QP /6

=> QP = 2.4 cm.

Hence , AB = 6cm & PQ = 2.4 cm.

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