# In the adjoining figure, P and Q are points on sides AB and AC respectively of mix such that PQ || BC and AP= 8 cm, AB =12 cm, AQ = 3x cm, QC = (x + 2) cm. Find x.

Given: AP = 8cm , AB =12cm, AQ = (3x)cm and QC = (x+2)cm

and PQ || BC

Basic Proportionality theorem which states that if a line is drawn parallel to one side of a triangle the other two sides in distinct points, then the other two sides are divided in the same ratio.

[by basic proportionality theorem]

2(x+2) = 3x

2x + 4 = 3x

2x – 3x = - 4

x = 4

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