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
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the three angles of a quadrilateral are 65 degree 55 degree and 130 degree . find its fourth angle.
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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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