In figure, M, N, and P are the mid-points of AB, AC and BC respectively. If MN = 3 cm, NP = 3. 5 cm and MP = 2.5 cm, calculate the length of BC, AB and AC

6 cm, 7 cm, 5 cm

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5 cm, 7 cm, 5 cm

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6 cm, 6 cm, 5 cm

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none of the above

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Solution

The correct option is A 6 cm, 7 cm, 5 cm
$S i n c e M, N, a n d P a r e t h e m i d - p o i n t s o f A B, A C a n d B C r e s p e c t i v e l y . H e n c e M N = \frac{1}{2} B C ⟹ B C = 2 M N ⟹ B C = 2 \times 3 = 6 c m S i m i l a r l y A C = 2 M P = 2 \times 2.5 = 5 c m a n d A B = 2 N P = 2 \times 3.5 = 7 c m$

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