Equilateral triangle ABC has a perimeter of 96 millimeters. A perpendicular bisector is drawn from angle A to side Line segment B C at point M. What is the length of Line segment M C? 16 mm 24 mm 32 mm 48 mm

The correct option is A. 16 mm.

Given, the perimeter of equilateral triangle is 96 mm.

We know that perimeter is the sum of all sides and all sides of equilateral triangle are equal .

So, one side of equilateral triangle will be,

.

Since the perpendicular bisector is drawn from angle A to side B C at point M.

Hence it bisect the BC in two equal parts.

so,the length of MC will be,

Hence the length of MC is 16 mm.

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Step-by-step explanation:

An equilateral triangle is a triangle that has all of its sides equal.

Perimeter of an equilaterial triangle = 3s where;

s is one side of the triangle.

Given the perimeter of ABC = 96mm

Substituting into the formula above to get s;

96 = 3s

s = 96/3

s = 32mm

Hence the length of one side of the triangle is 32mm

If a perpendicular bisector is drawn from angle A to side Line segment B C at point M, then MC will be half of BC and ΔAMC will be a right angled triangle.

Since all the sides of the triangle are equal, hence BC = 32mm. Since MC is the half of BC, then MC = 1/2 of 32mm

MC = 1/2 * 32mm

MC = 16mm

Hence the length of Line segment MC is 16mm

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