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

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calculista calculista · Answer 1 · 2018-09-25T17:33:52+02:00

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

[tex]AB=BC=AC=16 units[/tex]

the height of the triangle is the segment BD

in the right triangle BCD

Applying the Pythagorean Theorem

[tex]BC^{2} =BD^{2}+DC^{2}[/tex]

solve for BD

[tex]BD^{2}=BC^{2}-DC^{2}[/tex]

substitute the values

[tex]BD^{2}=16^{2}-8^{2}[/tex]

[tex]BD^{2}=192[/tex]

[tex]BD=\sqrt{192}\ units[/tex]

therefore

the answer is

the height of the triangle is [tex]\sqrt{192}\ units[/tex]

boffeemadrid boffeemadrid · Answer 2 · 2019-02-13T08:46:40+01:00

Answer:

The height of an equilateral triangle will be =[tex]\sqrt{192}units[/tex]

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

[tex](MO)^{2}=(OD)^{2}+(MD)^{2}[/tex]

[tex](16)^{2}=(8)^{2}+(MD)^{2}[/tex]

[tex]256=64+MD^{2}[/tex]

[tex]256-64=(MD)^{2}[/tex]

[tex]MD=\sqrt{192}[/tex]

Therefore, the height of an equilateral triangle will be =[tex]\sqrt{192}units[/tex].