Please solve q 104 ?

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Answer 1 · 2018-05-26T02:03:13

#(2) " " sqrt17# units

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Let #G# be the centroid where medians #AD and BE# meet.

As #AG:GD=BG:GE=2:1#,

let #AG=2y, => GD=y#,

let #BG=2x, => GE=x#

In #DeltaBGD, (2x)^2+y^2=(7/2)^2#

#=> 4x^2+y^2=(49)/4 ----- Eq(1)#

In #DeltaAGE, x^2+(2y)^2=3^2#,

#=> x^2+4y^2=9 ----- Eq(2)#

Adding #Eq(1) and Eq(2)# together, we get:

#5x^2+5y^2=49/4+9#

#=> 5(x^2+y^2)=85/4#

#=> color(red)(x^2+y^2=17/4)#

In #AGB, AB^2=(2x)^2+(2y)^2#

#=> AB^2=4(x^2+y^2)=4*(17)/4=17#

#=> AB=sqrt17# units