Question

If the area of equilateral triangle is 3√3 cm square then find the height of the equilateral triangle

Answer 1

Answer:

3

Step-by-step explanation:

Area of equilateral triangle = (√3/4)*a^2

which is equal to 3√3 (given)

So 'a' comes to be 2√3

Now Area of Triangle is also 1/2 * base * height

base='a'=2√3

So height comes as 3

Answer 2

Answer: 3 cm

Step-by-step explanation:

Area of an equilateral triangle = (√3/4)a^2

(√3/4)a^2=3√3

THEREFORE,

a^2= (3√3)(4)/√3

a^2= 12

Therefore, a= √12= 2√3 cm

Now, a = 2√3

a/2 = (2√3)/2= √3 cm

Therefore a= AB= 2√3 cm

BD= √3 cm

Therefore height = AD = ?

ACCORDING TO PYTHAGORAS THEOREM,

AB^2= AD^2+BD^2

Therefore, AD^2=AB^2-BD^2

AD^2= (2√3)^2-(√3)^2

AD^2 = 12-3 = 9 cm

Therefore,

AD= √9 = 3 cm

Therefore , the height of the equilateral triangle is 3 cm.

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