SOLUTION: if the perimeter of an equilateral triangle be 18cm,then the length of each median is

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Question 921402: if the perimeter of an equilateral triangle be 18cm,then the length of each median is
Answer by MathLover1(20849) About Me  (Show Source):
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an equilateral triangle has all sides equal length
so,the perimeter is P=3a where a is side
if the perimeter of an equilateral triangle be P=18cm,then
18cm=3a
18cm%2F3=a
6cm=a
the median divides equilateral triangle into two right angle triangle where the median is one leg, a%2F2 is the other leg, and a is hypotenuse; so, use Pythagorean theorem

a%5E2=median%5E2%2B%28a%2F2%29%5E2 ..............plug in 6cm=a

%286cm%29%5E2=median%5E2%2B%286cm%2F2%29%5E2

36cm%5E2=median%5E2%2B%283cm%29%5E2

36cm%5E2-9cm%5E2=median%5E2

25cm%5E2=median%5E2

sqrt%2825cm%5E2%29=median

5cm=median => the length of each median; in an equilateral triangle all three median are congruent