Question

each side of an equilateral triangle is 6cm. find the length of its altitudes.

Answer 1

Hi Mate!!!!

let the length of altitude be x

By Pythagoras theorem


( 6 )² = ( 3 )² + ( x )²

x² = 25

x = √ 25 or x = -√ 25

x = 5 or x = -5


x = -5 is rejected becoz length can't be -ive


so, length of altitude is 5cm

Answer 2

hey mate here's ur answer

given :

each side of eq. ∆ ABC = 6 cm

let's draw an altitude AD on side BC.

now area of ∆ ABC = √3/4(side)²

= √3/4(6)²

= √3/4*36

= 9√3 cm²

now area of ∆ ABD = 1/2 area of ∆ ABC

=> 1/2*b*h = 9√3/2

=> 1/2*3*h = 9√3/2

=> h = (9√3/2)*(2/3)

=> h = 3√3

so, altitude of ∆ = 3√3 cm


alternatively :

By using Pythagoras theorem,

AB² = BD² + AD²

6² = 3² + AD²

AD² = 36 - 9

AD² = 27

AD = 3√3