Question

Find the height of an équilateral
triangle having side 2a
​

Answer 1

Answer:

side of the equilateral triangle is 2a

so,area of the triangle is √3/4.side^2=√3/4.(2a)^2

=√3/4.4a^2=√3a^2

let the height of the equilateral triangle is h

so,1/2.base.height=area

=> 1/2.2a.h=√3a^2

=> a.h=√3a^2

=> h=√3a^2/a

=> h=√3a

so,height of the equilateral triangle is √3a unit

Answer 2

Answer:-

• Length of altitude = a√3

Step-by-step explanation:

Given : Side of equilateral triangle = 2a

To find : Length of height of triangle

Solution :

Let's consider a triangle ABC where each side is of 2a length.

Now drop a perpendicular from A on side BC at a point D.

Now,

Distance of CD = BD = a ( as perpendicular in a equilateral triangle divides the side in equal length).

Now triangles ABD and ACD are equilateral triangle.

Applying Pythagoras theorem in ∆ ABD (any of the ∆).

→ AB² = AD² + BD²

→ (2a)² = AD² + (a)²

→ 4a² = AD² + a²

→ 4a² - a² = AD²

→ 3a² = AD²

→ √(3a²) = AD

→ a√3 =AD

So the length of altitude of triangle = a√3.