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Question

In the given 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, find the length of BC, AB, and AC.

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Solution

Here, MN is a line which joins the mid-point M of AB and N of AC.

Then, by mid-point theorem, MNBC and MN=12BC
BC=2MN=6 cm

Similarly, ACMP and MP=12AC
AC=2MP=5 cm

And, ABNP and NP=12AB
AB=2NP=7 cm

So, the length of the sides BC, AB, and AC are 6 cm, 7 cm, and 5 cm, respectively.

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