Question

△LMN is an equilateral triangle. Find side of triangle if height LD is 2√3 cm.​

Answer 1

Step-by-step explanation:

Given: height of equilateral triangle is2√3 cm

According to the question ,

√3/2*side of equilateral triangle= height of equilateral triangle

side= 2√3*2/√3

side= 4 cm

Side of a triangle is 4cm

Answer 2

Answer:

The side of the triangle is 4 cm

Step-by-step explanation:

Given that Δ LMN is an equilateral triangle

=> All the sides of the triangle are equal

Given that the height of the triangle is LD = 2√3 cm.​

Let the each side of the triangle be '2a' cm

=> LM = MN = NL = 2a cm

We know that the height of an equilateral triangle divides the base in equal halves.

=> MD = DN = 2a/2 = a cm

Therefore, in Δ LDN

(see the picture for reference)

(LD)² + (DN)² = (NL)²

On substituting the values,

=> (2√3)² + (a)² = (2a)²

=> 12 + a² = 4a²

=> 12 =  4a² - a²

=> 12 = 3a²

=> 4 = a²

=> a = ± 2

As it is length, it cannot be negative,

Therefore, a = 2

and 2a = 2*2 = 4

Therefore, the side of the triangle = 2a = 4 cm