ΔABC is an equilateral triangle of side 2a units. Find each of its altitudes.

Question

Philoid · Accepted Answer

Δ ABC is an equilateral triangle.

Also, BC = AB = AC = 2a

The AD, CE, and BF are the altitude at BC, AB and AC respectively. Therefore, D, E, and F are the midpoint of BC, AB and AC respectively.

Now, ΔADB and ΔADC are right-angled triangles.

Applying Pythagoras theorem,

AB² = BD² + AD²

⇒ (2a) ² = a² + AD²

⇒ AD² = 3a²

⇒ AD = a√3 units

Similarly ΔACE and ΔBEC are right-angled triangles.

Applying Pythagoras theorem,

CE = a√3 units

And ΔABF and ΔBFC are right-angled triangles.

Applying Pythagoras theorem,

BF = a√3 units