In ΔABC,D is the median from A to BC.AB = 6cm, AC = 8cm, and BC = 10cm. The length of median AD (in cm) is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 5.
Pythagoras theorem
AB2 + AC2 = BC2
Circumcentre theorem
Circumcentre of a right-angled triangle lies on the mid-point of the hypotenuse
AD = BD = DC
Calculation:
AB2 + AC2 = BC2
62 + 82 = 102
Hence, Pythagoras' theorem is applicable here
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 = 5cm
AD = BD = DC = 5cm.
Hence,
The length of the median AD is 5 cm