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# In the rectangle above, A is the midpoint of the side, and

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Re: In the rectangle above, A is the midpoint of the side, and [#permalink]
well u wld hve to b a lil patient wid me...

somehow um still unclear with the explanation
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Re: In the rectangle above, A is the midpoint of the side, and [#permalink]
DeeptiM
well u wld hve to b a lil patient wid me...

somehow um still unclear with the explanation

D from my side.

1. Area of rectangle = 2*2*Area(AOB) - Suff.
2. Area of rectangle = 2*3*Area COD (because Area BOC= Area COD= Area DOC) - Suff.

Hope it helps.

Cheers,
Aj.
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Re: In the rectangle above, A is the midpoint of the side, and [#permalink]
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DeeptiM
In the rectangle above, A is the midpoint of the side, and BC=CD=DE. What is the area of the rectangle?
(1) The area of the shaded region is 24.
(2) The area of triangle CDO is 16.

I got the answer but need a more concise approach..

Attachment:
Geomtery_Median_DS.JPG

Let's call the vertex diagonally opposite of E as F.

1.
OA is the median of $$\triangle OBF$$, because A is the mid-point of FB. A median divides a triangle in two-halves such that the areas of two newly formed triangles are equal.

Area(OAF)=Area(OAB)=24
Area(OBF)=2*Area(OAB)=2*24=48

A diagonal of a rectangle divides the rectangle in two equal halves such that the area remains same for both halves.

Thus, Area(ABEO)=2*Area(BOF)=2*48=96
Sufficient.

2.
Same concept as statement 1.
OD is the median of OCE because CD=DE
AND
OC is the median of OBD because CD=BC

Area(ODE)=Area(OCD)=Area(OCB)=16
Area(OBE)=3*16=48
Area(FBEO)=2*Area(OBE)=2*48=96
Sufficient.

Ans: "D"
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Re: In the rectangle above, A is the midpoint of the side, and [#permalink]
Vijayeta
Need a explanation of this.
https://pasteboard.co/Ij3uxKD.jpg (click the url to see my solution)

Just labelling the sides of the rectangle as 2x (for the side having point A) and 3y (for the side having pts B,C,D) does the trick. No complex calculation needed in this question.
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Re: In the rectangle above, A is the midpoint of the side, and [#permalink]
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Re: In the rectangle above, A is the midpoint of the side, and [#permalink]
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