Question 74

In ABC, P and Q are the middle points of the sides AB and AC respectively. R is a point on the segment PQ such that PR : RQ = 1 : 2. If PR= 2 cm. then BC =

Solution

$$ \frac{PR}{RQ} =\frac{1}{2} $$ (given)

PR = 2 cm

$$ \frac{2}{RQ} = \frac{1}{2} $$

solving, RQ = 4 cm

PQ = PR + RQ = 2 + 4 = 6 cm

As the line joining the mid points of 2 sides of a triangle is parallel and half of the third side

therefore, BC = 2PQ = $$ 2 \times 6 = 12 cm $$

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