In the rectangle above, A is the midpoint of the side, and BC = CD = DE. What is the area of the rectangle?

The area of a rectangle is (width)*(length).

Notice that since A is the midpoint of the width of the rectangle, then AB = (width)/2
Also, since BC = CD = DE, then CD = (length)/3.

(1) The area of the shaded region is 24. The area of the shaded triangle = 1/2*BE*AB = 1/2*(length)*(width)/2 = 24 --> (length)*(width) = 96. Sufficient.

(2) The area of triangle CDO is 16. The area of triangle CDO = 1/2*OE*CD = 1/2*(width)*(length)/3 = 16 --> (width)*(length) = 96. Sufficient.

Answer: D.

Hope it's clear.
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well u wld hve to b a lil patient wid me...

somehow um still unclear with the explanation

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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A question,

assume that the upper left vertice is called X. So according to 1) since B is the mid point, would it be correct to assume that the shaded region has the same area as AXO? So the shaded region is 1/4th of the whole rectangle.

Same goes to 2) since the base is 1/3rd of the length, so the region CDO is 1/3rd of the "lower" right triangle BOE and 1/6th of the rectangle.

Am I correct?