Question

Inis triangle ABCthe midpoint of BC. E is the foot of the perpendicular from A to BC (lie on BC), and F is the foot of the perpendicular from D to AC. Given that BE=5 EC=9
and the area of triangle ABC is 84. Then the value of EF i​

Answer 1

Let DE and DF be the perpendiculars from D on AB and AC respectively.

In △s BDE and CDF, DE=DF (Given)

∠BED=∠CFD=90

∘

BD=DC (∵ D is the mid-point of BC)

∴ △BDE≅△CDF (RHS)

⇒ ∠B=∠C (cpct)

⇒ AC=AB (Sides opp. equal ∠s are equal)

⇒ △ABC is isosceles.