Question : In $\triangle A B C,$ P and Q are the middle points of the sides AB and AC, respectively. R is the point on the segment PQ such that PR : RQ = 1 : 3. If PR = 6 cm, then BC is:
Option 1: 46 cm
Option 2: 48 cm
Option 3: 44 cm
Option 4: 50 cm
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Correct Answer: 48 cm
Solution :
Given, PR ∶ RQ = 1 ∶ 3 and PR = 6 cm
Let the PR and RQ be $x$ and $3x$ respectively.
According to the question,
⇒ PR = $x$ = 6 cm [Given]
⇒ RQ = $3x$ = 3 $×$ 6 = 18 cm
Now,
⇒ PQ = (PR + RQ)
⇒ PQ = (6 + 18) cm
⇒ PQ = 24 cm
We know that the line joining the midpoints of two sides of a triangle is parallel and half of the third side.
So, BC = 2PQ = 2 $×$ 24 = 48 cm
Hence, the correct answer is 48 cm.
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