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Addition of vectors

In a traingle...

Question

In a traingle $A B D$ , $E, F, G$ are mid points of sides $A B, B D, D A$ respectively. $C$ represents the centroid of the triangle. If $B C = 9, C G = 2 x + 1$ , Find $x$ ,

1.75

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2.75

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1.25

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2.25

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Solution

The correct option is A $1.75$

$B C = 9, C G = 2 x + 1$
$B C = \frac{2}{3}$ BG
$9 = \frac{2}{3} (2 x + 1 + 9)$
$9 = \frac{2}{3} (2 x + 10)$
$\frac{27}{2}$ =2x+10 $\Rightarrow$ 2x= $\frac{27}{2}$ -10 $\Rightarrow$ 2x= $\frac{7}{2}$
$x = \frac{7}{4}$ $\Rightarrow$ x=1.75$
Hence, $1.75$ is the correct answer.

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In a traingle ABD, E,F,G are mid points of sides AB,BD,DA respectively. C represents the centroid of the triangle. If BC=9,CG=2x+1, Find x,

The correct option is A 1.75BC=9,CG=2x+1BC=23BG9=23(2x+1+9)9=23(2x+10)272=2x+10⇒2x=272-10⇒2x=72x=74⇒x=1.75$Hence, 1.75 is the correct answer.

In a traingle $A B D$ , $E, F, G$ are mid points of sides $A B, B D, D A$ respectively. $C$ represents the centroid of the triangle. If $B C = 9, C G = 2 x + 1$ , Find $x$ ,