Q4 of 53 Page 156

In ΔABC AB = 7, AC = 5, AD = 5. Find , if the mid – point of BC is D.

4-2.JPG


D is the mid – point of BC


AB = 7


AC = 5


AD = 5


Let BD = x


Applying Appoloneus theorem :


AB2 + AC2 = 2(AD2 + BD2)


⇒ 72 + 52 = 2(52 + x2)


⇒ 74 = 50 + 2x2


⇒ 2x2 = 24


⇒ x2 = 12


⇒ x = 2√3 units


BC = 2 × BD = 4√3 units


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