In a triangle ABC, P and Q are the points on the sides AB and AC such that PQ ‖‖ BC. Find the value of x, if AP = x, AQ = x + 3, PB = x + 1, QC = x + 5. (a) x = 4 (b) x = 5 (c) x = 3 (d) x = 2
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In a △ABC,P and Q are the points on sides AB and BC respectively, such that PQ∥BC. Also, AP=2 cm,PB=4 cm,AQ=3 cm and QC=6 cm then find BC
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Let ABC be a triangle. Let P,Q are the points on sides AB,BC respectively such that PQ∣∣BC.
Given AP=2cm,PB=4cm,AQ=3cm,QC=6cm.
We have to find BC.
The pictorial representation of the problem is shown below
Since we have PQ∣∣BC we get ΔAPQ∼ΔABC
⇒
AB
AP
=
AC
AQ
=
BC
PQ
Substituting the values we get,
⇒
6
2
=
9
3
=
BC
PQ
⇒
3
1
=
3
1
=
BC
PQ
⇒
3
1
=
BC
PQ
⇒BC=3PQ
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