Respuesta :
Answer:
Correct option: First one -> 16 mm
Step-by-step explanation:
The equilateral triangle has its three sides with the same length.
So if the perimeter is 96 mm, we have:
[tex]Perimeter = 3*side[/tex]
[tex]3*side = 96[/tex]
[tex]side = 32 mm[/tex]
The segment MA is the height of the equilateral triangle, and its length can be calculated with the equation:
[tex]height = \frac{side * \sqrt{3}}{2}[/tex]
[tex]height = 16\sqrt{3}[/tex]
Using the Pythagoras' theorem in the triangle ACM, we have:
[tex]side^2 = MC^2 + height^2[/tex]
[tex]1024 = MC^2 + 768[/tex]
[tex]MC^2 = 256[/tex]
[tex]MC = 16\ mm[/tex]
Correct option: First one
