Q17 of 95 Page 5

Find the height of an equilateral triangle of side 12 cm.


Given: ABC is an equilateral triangle


∴ AB = AC = BC = 12cm


And let AD is an altitude on BC. Therefore,


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 cm


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