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14 Oct 2017, 22:55
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C
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Difficulty:
35%
(medium)
Question Stats:
74% (02:25) correct
26%
(02:43)
wrong
based on 72
sessions
History
Date
Time
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Not Attempted Yet
In the given figure, ABCD is a rectangle. P and Q are midpoints of the side CD and BC respectively. Then the ratio of area of shaded region to non shaded one is?
A. 5:4
B. 4:3
C. 5:3
D. 8:3
E. 3:5
A. 5:4
B. 4:3
C. 5:3
D. 8:3
E. 3:5
Attachments
File comment: Figure
abcd rectangle.jpg [ 129.06 KiB | Viewed 9410 times ]
14 Oct 2017, 23:13
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ss3617
As values of sides of rectangle is not given and we need to calculate the ratio, we can assume Smart numbers for easy calculation.
Let length of rectangle \(AB=DP=40\) and width \(AD=BC=20\)
Hence area of rectangle \(= 40*20=800\)
Area of non-shaded region \(= 800-\)area of shaded region
so \(DP=PC=20\) and \(BQ=CQ=10\)
Now its easy to calculate areas of shaded regions which are right angle triangles ADP, CPQ and ABQ
the area of ADP\(=\frac{1}{2}*20*20=200\)
area of CPQ\(= \frac{1}{2}*20*10=100\)
area of ABQ\(=\frac{1}{2}*40*10=200\)
Hence area of shaded region \(= 200+200+100=500\)
area of non shaded region \(= 800-500=300\)
So ratio \(= \frac{500}{300}=5:3\)
Option C
15 Oct 2017, 00:23
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A more simpler way would be to assume it a square of side 1.
(Since square is also a rectangle with length = breadth)
Shaded Portion = Area(ADP) + Area(ABQ) + Area(PCQ)
\(= 1/4 + 1/4 + 1/8\)
\(= 5/8\)
Area of Un-shaded Portion = 1 - Area (Shaded)
\(= 3/8\)
Ratio: 5/3
C.
(Since square is also a rectangle with length = breadth)
Shaded Portion = Area(ADP) + Area(ABQ) + Area(PCQ)
\(= 1/4 + 1/4 + 1/8\)
\(= 5/8\)
Area of Un-shaded Portion = 1 - Area (Shaded)
\(= 3/8\)
Ratio: 5/3
C.
