Question

Find the altitude of an equilateral triangle of side 8 cm.

Answer 1

Let ABC be an equilateral triangle of side 8 cm

AB = BC = CA = 8 cm ...(All sides of an equilateral triangle is equal)

Draw altitude AD which is perpendicular to BC.

Then, D is the mid-point of BC.

∴ BD = CD = `1/2`

BC = `8/2` = 4 cm

Now, by Pythagoras theorem

AB² = AD² + BD²

⇒ (8)² = AD² + (4)²

⇒ 64 = AD² + 16

⇒ AD = 64 – 16 = 48

⇒ AD = `sqrt(48)` = `4sqrt(3)` cm.

Hence, altitude of an equilateral triangle is `4sqrt(3)` cm.