Question

Find the altitude of an equilateral traingle of side 8 cm​

Answer 1

$\bf\huge\underline{Question}$

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

$\bf\huge\underline{Solution}$

Let ABC be an equilateral traingle of side 8 cm i.e., AB = BC = CA = 8 cm

Draw altitude AD which is perpendicular to BC. Then, D is the mid-point of BC.

Therefore, BD = CD = $\dfrac{1}{2}$BC = $\dfrac{8}{2}$ = 4 cm

Now, AB² = AD² + BD²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀[by Pythagoras theorem]

=> (8)² = AD² + (4)²

=> 64 = AD² + 16

=> AD² = 64 - 16 = 48

=> AD = $\sqrt{48}$ = 4$\sqrt{3}$ cm

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