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In the given figure, ABCD is a rectangle. P and Q are midpoints

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In the given figure, ABCD is a rectangle. P and Q are midpoints  [#permalink]

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New post 14 Oct 2017, 22:55
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  25% (medium)

Question Stats:

78% (01:59) correct 22% (01:58) wrong based on 58 sessions

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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

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In the given figure, ABCD is a rectangle. P and Q are midpoints  [#permalink]

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New post 14 Oct 2017, 23:13
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ss3617 wrote:
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


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
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Re: In the given figure, ABCD is a rectangle. P and Q are midpoints  [#permalink]

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New post 15 Oct 2017, 00:23
2
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.
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Re: In the given figure, ABCD is a rectangle. P and Q are midpoints  [#permalink]

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New post 15 Oct 2017, 00:55
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=40AB=DP=40 and width AD=BC=20AD=BC=20

Hence area of rectangle =40∗20=800=40∗20=800

Area of non-shaded region =800−=800−area of shaded region

so DP=PC=20DP=PC=20 and BQ=CQ=10BQ=CQ=10

Now its easy to calculate areas of shaded regions which are right angle triangles ADP, CPQ and ABQ

the area of ADP=12∗20∗20=200=12∗20∗20=200

area of CPQ=12∗20∗10=100=12∗20∗10=100

area of ABQ=12∗40∗10=200=12∗40∗10=200

Hence area of shaded region =200+200+100=500=200+200+100=500

area of non shaded region =800−500=300=800−500=300

So ratio =500300=5:3=500300=5:3

Option C
Re: In the given figure, ABCD is a rectangle. P and Q are midpoints &nbs [#permalink] 15 Oct 2017, 00:55
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