Q18 of 168 Page 4

In an equilateral triangle ABC, if, then

Given in equilateral ΔABC, AD ⊥ BC.



We know that the Pythagoras theorem state that in a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.


In ΔABD,


⇒ AB2 = AD2 + BD2


⇒ AB2 = AD2 + ( 1/2BC)2 [∵ BD = 1/2BC]


⇒ AB2 = AD2 + ( 1/2AB)2 [∵ AB = BC]


⇒ AB2 = AD2 + 1/4AB2


∴ 3AB2 = 4AD2

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