How To Find The Length Of Mc In An Equilateral Triangle With A Perimeter Of 96Mm – A Step-By-Step Guide

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

a

First, we need to find the length of each side of the equilateral triangle. Since the triangle is equilateral, all sides are equal in length.

Let x be the length of each side of the equilateral triangle.

Perimeter = 96 mm

Therefore,

3x = 96

x = 32

Now we need to find the length of MC.

From point A, draw a perpendicular bisector to BC and mark the intersection point as M. This perpendicular bisector divides the equilateral triangle into two congruent 30-60-90 triangles.

The length of the side opposite the 60-degree angle in a 30-60-90 right triangle is √3 times the length of the shorter leg.

So, in triangle AMC, the length of MC is

MC = AC/2

Since AC is the longer leg, we have:

AC = 2 * AM

But, AM is also the height of the equilateral triangle, i.e. √3/2 x

Therefore,

AC = 2 * AM = 2 * (√3/2 x) = √3 x

MC = AC/2 = (√3 x)/2 = (√3)/2 * 32 = 16√3

Using a calculator, we get:

MC ≈ 27.7 mm

Therefore, the length of line segment MC is approximately 27.7 mm.

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