Question

find the side and perimeter of an equilateral triangle whose height is ✓6 cm​

Answer 1

Since, ABC is an equilateral triangle, CD is the perpendicular bisector of AB. Hence, the length of the side of an equilateral triangle is 2 cm. Hence, perimeter of an equilateral triangle is 6 cm.

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Answer 2

Given,

Altitude = √3 cm

Let the ΔABC be equilateral triangle.

All angles will be 60°.

And Altitude (AD) will bisect the base.

So, ∠ADC = 90°.

Let the side be a. Then, by pythagoras theorem in ΔADC,

Altitude² + (a/2)² = a²

3² = a²- a²/4

3 = 3a²/4

a² = 4

a = 2 cm

Now,

Perimeter = 3 * side

                 = 3 * 2 cm

                = 6 cm

Hope It Helps You :)