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