Question : If the perimeter of an equilateral triangle is 18 cm, then the length of each median is:
Option 1: $3\sqrt2$ cm
Option 2: $2\sqrt3$ cm
Option 3: $3\sqrt3$ cm
Option 4: $2\sqrt2$ cm
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Correct Answer: $3\sqrt3$ cm
Solution :
Let $a$ be the side of the triangle.
The perimeter of an equilateral triangle = 18 cm
$3a=18$
$\therefore a=\frac{18}{3}=6$ cm
So, length of the median $=\frac{\sqrt3a}{2}=\frac{\sqrt3×6}{2}=3\sqrt3$ cm
Hence, the correct answer is $3\sqrt3$ cm.
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