In a triangle ABC if the equation of the medians AD and BE are 2x+3y-6=0 and 3x-2y-10=0 respectively and AD=6,BE=11 , then the area of triangle ABC , is

Question

In a triangle ABC if the equation of the medians AD and BE are 2x+3y-6=0 and 3x-2y-10=0 respectively and AD=6,BE=11 , then the area of triangle ABC , is (A) 1 (B) 22 (C) (44/3) (D) 44

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-2ao5w5hm2navoqd9.jpg" /> Let G is centroid AG=(2/3)AD=(2 × 6/3)=4 BG=(2/3)BE=(2 × 11/3)=(22/3) Area of Δ ABC=3× (Area of Δ AGCB ) =3× ((1/2) × 4 × (22/3)) =44squnit

Q. In a triangle $A BC$ if the equation of the medians $A D$ and $BE$ are $2 x + 3 y - 6 = 0$ and $3 x - 2 y - 10 = 0$ respectively and $A D = 6, BE = 11$ , then the area of triangle $A BC$ , is

$1$

$22$

$\frac{44}{3}$

$44$

Let $G$ is centroid $A G = \frac{2}{3} A D = \frac{2 \times 6}{3} = 4$
$BG = \frac{2}{3} BE = \frac{2 \times 11}{3} = \frac{22}{3}$
Area of $Δ A BC = 3 \times$ (Area of $Δ A GCB$ )
$= 3 \times (\frac{1}{2} \times 4 \times \frac{22}{3})$
$= 44 s q u ni t$

Q. In a triangle ABC if the equation of the medians AD and BE are 2x+3y−6=0 and 3x−2y−10=0 respectively and AD=6,BE=11 , then the area of triangle ABC , is

1

22

344​

44

Let G is centroid AG=32​AD=32×6​=4 BG=32​BE=32×11​=322​ Area of ΔABC=3× (Area of ΔAGCB ) =3×(21​×4×322​) =44squnit

Q. In a triangle $A BC$ if the equation of the medians $A D$ and $BE$ are $2 x + 3 y - 6 = 0$ and $3 x - 2 y - 10 = 0$ respectively and $A D = 6, BE = 11$ , then the area of triangle $A BC$ , is

$1$

$22$

$\frac{44}{3}$

$44$

Let $G$ is centroid $A G = \frac{2}{3} A D = \frac{2 \times 6}{3} = 4$
$BG = \frac{2}{3} BE = \frac{2 \times 11}{3} = \frac{22}{3}$
Area of $Δ A BC = 3 \times$ (Area of $Δ A GCB$ )
$= 3 \times (\frac{1}{2} \times 4 \times \frac{22}{3})$
$= 44 s q u ni t$