Question

triangle MNO is an equilateral triangle with sides measuring 16 units What is the height of the triangle?

Answer 1

see the attached figure to better understand the problem

we know that

The equilateral triangle has three equal sides

so

in the equilateral triangle ABC

$AB=BC=AC=16 units$

the height of the triangle is the segment BD

in the right triangle BCD

Applying the Pythagorean Theorem

$BC^{2} =BD^{2}+DC^{2}$

solve for BD

$BD^{2}=BC^{2}-DC^{2}$

substitute the values

$BD^{2}=16^{2}-8^{2}$

$BD^{2}=192$

$BD=\sqrt{192}\ units$

therefore

the answer is

the height of the triangle is $\sqrt{192}\ units$

Answer 2

Answer:

The height of an equilateral triangle will be =$\sqrt{192}units$

Step-by-step explanation:

It is given that triangle MNO is an equilateral triangle with sides measuring 16 units that is MN=NO=OM=16.

Now, Let MD be the height of an equilateral triangle, then applying the Pythagoras theorem in triangle MDO, we get

$(MO)^{2}=(OD)^{2}+(MD)^{2}$

$(16)^{2}=(8)^{2}+(MD)^{2}$

$256=64+MD^{2}$

$256-64=(MD)^{2}$

$MD=\sqrt{192}$

Therefore, the height of an equilateral triangle will be =$\sqrt{192}units$.