Question

If each side of an equilateral triangle is 6√3 , then, find the altitude of an equilateral triangle.

Answer 1

Answer:

Step-by-step explanation:

as we know in an equilateral triangle a altitude acts like a median

so In ΔABC AM is altitude on side BC

∴ BM = CM ------------ as AM will be median

In right angled ΔAMB

∠M = 90 ------- AM is Altitude

AB = 6√3 ------ given

BM = BC / 2 -------- as AM is Median

BM = 6√3/2

BM = 3√3

AB² = AM² + BM²-------- Pythagoras Theorem

AM² = AB² - BM²

AM² = (6√3)² - (3√3)²

AM² = 36 × 3 - 9 × 3

AM² = 108 - 27

AM² = 81

AM = √81

AM = 9

Therefore length of altitude is 9 cm

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