1.

In ∆ ABC, P and Q are points on sides AB and AC respectively such that, PQ || BC, if AP = 12 cm, PB = 8 cm, AQ = 9 cm, Find AC​

Answer»

Solution :-

In ΔABC,

P and Q are points on side AB and AC such that PQ||BC

Here, AP = 12cm, PB = 8cm, AQ = 9 cm .

[ If a line is drawn parallel to the one side of a TRIANGLE to intersect the other two sides in DISTINCT points, The other two sides are divided in the same ratio ]

Therefore,

AP / PB = AQ / QC

Let the QC be x cm

12/8 = 9/x

[ By cross multiply ]

12x = 72

x = 72/12

x = 6cm

Now,

We have to FIND AC

Therefore,

AC = AQ + QC

AC = 9 + 6

AC = 15cm

Hence, The value of AC is 15 cm .

Know More :-

• By converse of BPT

If a line divides any two sides of a triangle in the same ratio, then the line parallel to the third side.


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