Question

AD is a median of ΔABC. AB²+AC²=148 and AD=7. Find BC

Answer 1

HELLO DEAR,

given that:- AD is medians of triangle on BC so, BD = DC , BC = (BD + DC) = 2BD and <D = 90,
[ figure is in the attachment]

now, by Pythagoras theorem.

IN ∆ ABD,

AB² = BD² + AD²
AB² = BD² + (7)²
AB² = BD² + 49------------( 1 )

similarly, IN ∆ ACD,

AC² = DC² + AD²
AC² = DC² + (7)²
AC² = DC² + 49-------------( 2 )


adding ------( 1 ) &------( 2 )
we get,

AB² + AC ² = BD² + 49 + DC² + 49
(AB² + AC²) = (BD² + DC²) + 98
148 = 2BD² + 98
2BD² = 148 - 98.
2BD² = 50
BD² = 25
BD = 5

hence, BC = 2BD = 10


I HOPE ITS HELP YOU DEAR,
THANKS