Question

find the length of side and perimeter of an equilateral triangle whose height is root 3 cm

Answer 1

Let ∆ ABC is equilateral triangle.
Seg AD is median.
Therefore in ∆ ABC,
Angle A=30 (as AD is median)
Angle B=90(as AD is median)
Angle C=60(as ∆ABC is equilateral triangle)
Therefore by 30-60-90 theorem.
AD=✓3/2 ×AC
✓3 = ✓3/2 × AC
✓3×2/✓3 = AC
Therefore 2cm = AC
it is equilateral triangle
Therefore perimeter=3×side
=3×2cm
= 6cm

Answer 2

Hey there!

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!