Question

Find the height of equilatoral traingel having side 2a​

Answer 1

Answer:

height is √3......of triangle

Answer 2

Given:-

Side of the equilateral triangle = 2a

Required answer:-

Height of the triangle

Solution:-

Let ABC be the given equilateral triangle and AL be the height.

Each side = AB = BC = AC = 2a

Since, the altitude and median are same in eq. triangle,

Therefore, LC = a

Now in right triangle ALC,

by Pythagoras theorem,

${AC}^{2} = {AL}^{2} + {LC}^{2}$

Let, AL be x,

$= > {2a}^{2} = {x}^{2} + {a}^{2}$

$= > 4 {a}^{2} - {a}^{2} = {x}^{2}$

$= > 3 {a}^{2} = {x}^{2}$

$= > x = \sqrt{3 {a}^{2} }$

$= > x = \sqrt{3} a$

$hence \: the \: altitude \: is \: \sqrt{3} x$