Question

In ΔABC, AB = 11 cm, AC = 17 cm, BC = 12 cm. Find the length of the median drawn from point A to BC.

• A. 13 cm
• B. 15 cm
• C. 9 cm
• D. 10 cm

Answer 1

The correct option is A 13 cm

Let AD be the median drawn from A to BC.
$\mathrm{BD}=\mathrm{DC}=\frac{\mathrm{BC}}{2}=\frac{12}{2}=6\mathrm{cm}{\mathrm{AB}}^2+{\mathrm{AC}}^2=2{\mathrm{AD}}^2+2{\mathrm{BD}}^2...\left[\mathrm{Apollonius}\mathrm{theorem}\right]{11}^2+{17}^2=2{\mathrm{AD}}^2+2{\left(6\right)}^{2}121+289=2{\mathrm{AD}}^2+722{\mathrm{AD}}^2=338{\mathrm{AD}}^2=169\mathrm{AD}=\sqrt{169}\mathrm{AD}=13cm$