Question

in a triangle ABC if BC=4 CA=5 AB=3 find length of median

Answer 1

It is given that the sides are respectively 3 ,4 and 5 units.

Hence , check for the presence of a right angle by the pythagoras theorem....

AB^ 2+ BC^2 = CA^2

i.e 9+16=25

Hence, it is a right angled triangle with hypotenuse of 5 units.

The median will divide the side CA in two equal parts,say CM=MA = 2.5 units .

By the pythagoras theorem --

CM^2 + MB^2 = BC^2,

where MB is the length of the median.

Therefore MB^2= BC^2 - CM^2.

i.e MB^2= (4)^2 + (2.5)^2

MB^2= 16-6.25

MB^2= 9.75

MB = sqrt(9.25)

MB = 3.04 ~ MB = 3 units

Hence , your answer is the length of the median is 3 units ..

please draw a triangle in a paper and verify the answer if satisfied.

Thank you ....

Answer 2

ANSWER:

CM^2 + MB^2 = BC^2, where MB is the length of the median. Therefore MB^2= BC^2 - CM^2. Hence , your answer is the length of the median is 3 units

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