DeeptiM wrote:

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"

_________________

~fluke

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