Question : In $\triangle$ABC, D is the median from A to BC. AB = 6 cm, AC = 8 cm, and BC = 10 cm.The length of median AD (in cm) is:
Option 1: 4.5
Option 2: 5
Option 3: 4
Option 4: 3
Correct Answer: 5
Solution :
AB = 6 cm
BC = 10 cm
AC = 8 cm
AD is the median bisects BC
Pythagoras theorem,
AB$^2$ + AC$^2$ = BC$^2$
Circumcentre theorem
Circumcentre of a right-angled triangle lies on the mid-point of the hypotenuse
AD = BD = DC
AB$^2$ + AC$^2$ = BC$^2$
$6^2 + 8^2 = 10^2$
Since it obeys the Pythagoras theorem
It is a right-angled triangle
Circumcentre of a right-angled triangle lies on the mid-point of the hypotenuse
AD = BD = DC
AD is a median which bisects BC into two equal parts
BD = DC = 5 cm
AD = BD = DC = 5 cm.
$\therefore$ The length of the median AD is 5 cm.
Hence, the correct answer is 5 cm.
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