Question

In a $\Delta ABC$, if AB = 8 cm, AC = 10 cm and BC = 14 cm, then the length of median AD drawn from point A on BC is equal to

• A. 6 cm
• B. $\sqrt{35}$ cm
• C. $\sqrt{33}$ cm
• D. 8 cm

Answer 1

The correct option is C $\sqrt{33}$ cm

D is the mid-point of BC.
$BD=BC=\frac{1}{2}\times 14=7$



$A{B}^2+A{C}^2=2(A{D}^2+B{D}^2)$
$=(8{)}^2+(10{)}^2=2[A{D}^2+(7{)}^2]$
$=64+100=2A{D}^2+98$
$=2A{D}^2=164-98$
$=2A{D}^2=66$
$=A{D}^2=33$
$=AD=\sqrt{33}cm$
Hence, the correct answer is option (c).