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"