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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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