Answer :

4.JPG


AB =


AM = 2.5


Applying Pythagoras theorem in ΔABM


AB2 = AM2 + BM2


BM2 = 10 – 6.25 = 3.75


Let CM = x


AC = x + 2.5


Applying Pythagoras theorem in ΔCBM


BC2 = BM2 + CM2


BC2 = x2 + 3.75 …Equation (i)


Applying Pythagoras theorem in ΔABC


AC2 = AB2 + BC2


(x + 2.5)2 = BC2 + 10


x2 + 6.25 + 5x = BC2 + 10


BC2 = x2 – 3.75 + 5x …Equation (ii)


Equating Equation (i) and Equation (ii)


x2 + 3.75 = x2 – 3.75 + 5x


5x = 7.5


x = 1.5


So CM = 1.5


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