Question

Two medians AD and BE of triangle ABC intersect at G at right angles . If AD = 9 cm , BE = 12 cm , find length of AB?

Answer 1

Medians of a triangle intersect in the ratio of 2:1
Length of AB = √(BD)2+(AD)2...... (1)
To find BD:
AD =AG:GD = 6:3
BE = BG:GE = 8:4

from triangle BDG
BD = √BG2+DG2.....(2)
= √82+32
=√64+9
= √73
assign value in equation (1)
AB = √(√73)2+(9)2
= √73+81
=√154

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