Question

Find the height of an equilateral triangle having side 4 cm. ?​

Answer 1

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Side of an equilateral triangle = 4cm.

Formula to find height of an equilateral triangle = side × (√3)/2

Therefore,

height = side × (√3)/2

height = 4 × (√3)/2

height = 2√3

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Answer 2

Given= side = 4cm

Construction= Draw a perpendicular or height perpendicular to base.

Prove = Find Height

Proof = So as we know that it is a equilateral triangle so , all sides are equal so all sides are 4 cm and all angles are of 60°

,so as we cut the triangle so the above angle will cut in equal angle in 30° and base side also divides in two equal half means , 4/2 = 2cm

,so as it is a perpendicular so it is 90° from base so We can use Pythagoras theorem.

By Pythagoras theorem:-

Hypotenuse = 4 cm

Base = 4/2 = 2cm

Perpendicular or Height = ?

Hypotenuse² = Perpendicular ² + Base²

4² = Perpendicular ² + 2²

8 = Perpendicular ² + 4

Perpendicular² = 8 - 4

Perpendicular² = 4

Perpendicular = √4

Perpendicular = 2cm

so answer is..

Perpendicular or Height = 2cm