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
24 mm
32 mm
48 mm

Respuesta :

Answer:

16 mm  

Step-by-step explanation:

Since ABC is an equilateral triangle, all three sides are the same length.  The perimeter is found by adding together all of these equal sides; letting x represent the length of a side of the triangle, this gives us

x + x + x = 96

Combining like terms,

3x = 96

Dividing both sides by 3,

3x/3 = 96/3

x = 32

Since AM is a perpendicular bisector, it splits BC into two congruent sections. This means the length of MC, half of BC, will be 32/2 = 16.

Option (B) is correct which is 24 mm

Step 1:

Find the length of each side.

Let the side be a,

3×a = 96mm

⇒ a = 96/3

⇒ a = 32 mm

Step 2:

Length of MC = length of BC/2      (As AM is a perpendicular bisector)

⇒ MC = 32/2 = 16 mm

Step 3:

Now, in the triangle, AMC, using Pythagoras theorem,

AC² = MC² + AM²

⇒ (32)² = MC² + (16)²

After solving,

⇒ MC = 16√3 = 27.77 mm

This is closest to option (B) which is 24 mm

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