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

Question

Philoid · Accepted Answer

Let LMN be an equilateral triangle of side 8 cm

LM = MN = NL = 8 cm. (all sides of an equilateral triangle is equal)

Draw altitude LD which is perpendicular to MN.

Then, D is the mid-point of MN.

∴ MD = ND = 1/2

MN = 8/2 = 4 cm

Now, by Pythagoras theorem

LM² = LD² + MD²

⇒ (8)² = LD² + (4)²

⇒ 64 = LD² + 16

⇒ LD = √48 = 4√3 cm.

Hence, altitude of an equilateral triangle is 4√3 cm.