Question

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

Answer 1

The height of an equilateral triangle will be =
`√(192)units`

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=√(192)`

Therefore, the height of an equilateral triangle will be =
`√(192)units`.

Answer 2

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=√(192)\ units`

therefore

the answer is

the height of the triangle is
`√(192)\ units`