Question

Find the hieght of an equilateral traingle whose perimeter is 12 cm

Answer 1

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Answer 2

Given: ABC is an equilateral triangle

∴ AB = AC = BC = 12cm And let AD is an altitude on BC. Therefore, BD = 1/2 x BC = 6 cm

Now, In ∆ADB, using Pythagoras theorem, we have (Perpendicular)2 + (Base)2 = (Hypotenuse)2

⇒ (AD)2 + (BD)2 = (AB)2

⇒ (AD)2 + (6)2 = (12)2

⇒ (AD)2 = 144 – 36

⇒ (AD)2 = 108

⇒ AD = √108

⇒ AD = 6√3

Hence, the height of an equilateral triangle is 6√3