Given: The length of the median of an equilateral triangle is √3 cm.

To find: The length of the side of the equilateral triangle.

Solution:

Step 1: Recall the properties of an equilateral triangle:

- All sides of an equilateral triangle are equal.
- All angles of an equilateral triangle are equal and each angle is 60 degrees.
- The median of an equilateral triangle is also the altitude and angle bisector.

Step 2: Let's draw an equilateral triangle ABC with median AD as shown below.



Step 3: We know that the median AD divides the equilateral triangle ABC into two congruent right triangles ABD and ACD.



Step 4: Using Pythagoras theorem in right triangle ABD, we can find the length of AB.

AB² = AD² - BD²

As per the given information AD = √3 cm.

We know that in an equilateral triangle, the median is half of the side. Hence, BD = AB/2.

Substituting the value of BD, we get:

AB² = (√3)² - (AB/2)²

AB² = 3 - (AB²/4)

AB² + AB²/4 = 3

(5/4)AB² = 3

AB² = 12/5

AB = √(12/5) cm

Step 5: Simplifying the above expression, we get:

AB = (2√15)/5 cm

Hence, the length of the side of the equilateral triangle is (2√15)/5 cm.

Answer: The length of the side of the equilateral triangle is (2√15)/5 cm.

We know that in equi. Δ height and median are the same,if any dought than draw a triangle and median and try to prove them congruent....u can prove it by sss criteria.......now u can use trigonometric functions....tan 30°or tan60° or use area of equilateral triangle......but ur answer is i think answer is 2............