Please solve q 104 ?

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Answer 1 · 2018-05-26T02:03:13

$(2) \sqrt{17}$ $(2) " " sqrt17$ units

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Let $G$ $G$ be the centroid where medians $A D and B E$ $AD and BE$ meet.

As $A G : G D = B G : G E = 2 : 1$ $AG:GD=BG:GE=2:1$ ,

let $A G = 2 y, \Rightarrow G D = y$ $AG=2y, => GD=y$ ,

let $B G = 2 x, \Rightarrow G E = x$ $BG=2x, => GE=x$

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