Question

What is the height of an equilateral triangle if the sides are 10

Answer 1

Answer:

The height of the equilateral triangle is $5\sqrt{3}\ units$

Step-by-step explanation:

we know that

An equilateral triangle has three congruent sides, and three congruent angles that each measure 60 degrees

To find out the height of an equilateral triangle, apply the Pythagoras Theorem in the right triangle ABD

Remember that the height of an equilateral triangle bisects the base.

see the attached figure to better understand the problem

$AB^2=AD^2+BD^2$

substitute the given values

$10^2=5^2+BD^2$

Solve for BD

$100=25+BD^2$

$BD^2=100-25$

$BD^2=75$

$BD=\sqrt{75}\ units$

simplify

$BD=5\sqrt{3}\ units$`

therefore

The height of the equilateral triangle is $5\sqrt{3}\ units$