A triangle ABC is made up of two sides AC and BC of dimension 8 cm and 10 cm respectively. A median of 5 m is drawn on the side BC. What is the dimension of the third side of the triangle?

## Answer

Correct Answer : a ) 6

Explanation :Drawing the schematic diagram of the triangle according to the given information

As AD is the median so it will divide the line BC into two equal parts

Thus, BD = DC = 5 m

According to Apollonius theorem, “the sum of the squares of any two sides of any triangle is equal to twice the sum of square of the half of third side and square of the median bisecting the third side”

Therefore, applying Appolonius theorem in ? ABC

AB^{2} + AC^{2} = 2(AD^{2} + BD^{2})

So,

AB^{2} + 64 = 2 (25 + 25)

AB^{2} = 100 – 64

AB^{2} = 36

AB = 6 m

Hence, (a) is the correct answer.

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