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In the rectangle above, A is the midpoint of the side, and [#permalink]
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15 Aug 2011, 02:57
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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.
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Re: In the rectangle above, A is the midpoint of the side, and [#permalink]
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15 Aug 2011, 06:58
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Consider this, area for triangle is BH/2.
the two bigger triangles have the same B & H, the three small triangles have the same base and height. thus we can say the three smaller triangles or the 2 larger are equal. with (1) or (2) we can see the area of the full rectangle is 96.
(18*3)*2 or (24*2)*2



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Re: In the rectangle above, A is the midpoint of the side, and [#permalink]
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15 Aug 2011, 07:10
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]
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15 Aug 2011, 08:08
DeeptiM wrote: 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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15 Aug 2011, 08:40
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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 midpoint of FB. A median divides a triangle in twohalves 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]
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31 Jul 2014, 03:16
Need a explanation of this.



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Re: In the rectangle above, A is the midpoint of the side, and [#permalink]
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31 Jul 2014, 07:33
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Vijayeta wrote: Need a explanation of this. 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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In the rectangle above, A is the midpoint of the side, and [#permalink]
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06 May 2016, 11:33
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?




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