Question

In an equilateral triangle of side 2a cm, calculate the length of its altitude.​

Answer 1

⊱✿ ANswER ✿⊰

Let the triangle be ABC with AD as its altitude. Then, D is the midpoint of BC.

In right-angled triangle ABD, we have:

AB² = AD² + DB²

AD² = AB² - DB² = 4a² - a²

= 3a²

AD = √3a

Hence, the length of the altitude of an equilateral triangle of side 2a cm is √3a cm.

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Answer 2

Let the triangle be ABC with AD as its altitude. Then, D is the midpoint of BC.

In right-angled triangle ABD, we have

Hence, the length of the altitude of an equilateral triangle of side 2a cm is √3a cm