Question

find the height of an equilateral triangle whose area is 10000

Answer 1

Let the side of equilateral triangle = a

So, Pythagoras therom,

→ h² = p² + b²

→ a² = p² + (a/2)²

→ p² = 3a²/4

So, p = √3a/2

( where, p is the height of equil. ∆ )

Now, area of ∆ is 10000

>> 1/2 x b x h = 10000

>> 1/2 x a x √3a/2 = 10000

>> √3a² = 10000

>> a² = 10000/√3

>> a = 100/3^¼

Hence, p = √3a/2 = √3/2 x a

→ p = √3/2 x (100/3^¼)

→ p = 100√3/2

→ p = 50√3 _________________(Ans.)

Hence, height of the equilateral triangle is 50√3 units.