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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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31 Jul 2014, 07:33
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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?
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.
General Discussion
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
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
