2In a triangle ABC, AB = 9, BC = 10, AC = 13 if G is centroid. The value of line GB is
(a) 25 (b) 20 (c) 310 (d) 3
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Hi,
By Appolonious Theorem:
If D be the mid point of the side AC
of the triangle BAC
. B
A_________D_________C
Draw the rough daigram triangle
BAC, join BD , D is the mid point of
AC
2(BD² + AD²)= BA²+BC²
2(BD² + 13²/2² )= 9²+10²
2(BD² + 169/4)= 81+100
BD²+169/4 = 181/2
BD² = 181/2 - 169/4
BD²= (362-169)/4
BD² = 193/4
BD= √193/2
BG = (2/3 )× (√193 /2)
= √193 /3
I hope this helps you.
Options given is wrong.
By Appolonious Theorem:
If D be the mid point of the side AC
of the triangle BAC
. B
A_________D_________C
Draw the rough daigram triangle
BAC, join BD , D is the mid point of
AC
2(BD² + AD²)= BA²+BC²
2(BD² + 13²/2² )= 9²+10²
2(BD² + 169/4)= 81+100
BD²+169/4 = 181/2
BD² = 181/2 - 169/4
BD²= (362-169)/4
BD² = 193/4
BD= √193/2
BG = (2/3 )× (√193 /2)
= √193 /3
I hope this helps you.
Options given is wrong.
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