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