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Question

In an equilateral triangle ABC, AD is the median from vertex A to the side BC, the length of median is 27 cm, then find the length of the equilateral triangle.

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Solution

We know that,
In an equilateral triangle the Median is also the Altitude.
Let the side of the triangle measure x cm
Using Pythagorean theorem

(27)2+(x2)2=x2
x2(x2)2=(27)2
3x24=27
x2=27×43
x2=36
x=6 cm

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