Question

Side of a equilateral triangle is 2a . Find the length of altitude.

Answer 1

Answer:

a√3 cm

Step-by-step explanation:

Side of a equilateral triangle = 2a

Draw a altitude Say x units

Base = a

Using Pythagoras theorem

x = (2a)² - a²

x = a√3 units

HOPE IT HELPS!!!!!!!

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.