Question

Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side BC at point

M.
What is the length of MC?
16 mm
0 24 mm
O 32 mm
O 48 mm

Answer 1

(A) 16mm

Explanation:

Answer 2

Correct option: First one -> 16 mm

Explanation:

The equilateral triangle has its three sides with the same length.

So if the perimeter is 96 mm, we have:

`Perimeter = 3*side`

`3*side = 96`

`side = 32 mm`

The segment MA is the height of the equilateral triangle, and its length can be calculated with the equation:

`height = (side * √(3))/(2)`

`height = 16√(3)`

Using the Pythagoras' theorem in the triangle ACM, we have:

`side^2 = MC^2 + height^2`

`1024 = MC^2 + 768`

`MC^2 = 256`

`MC = 16\ mm`

Correct option: First one