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

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Manager
Joined: 17 Jul 2017
Posts: 109
Location: India
WE: Engineering (Transportation)
In the given figure, ABCD is a rectangle. P and Q are midpoints [#permalink]

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14 Oct 2017, 22:55
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Question Stats:

76% (01:54) correct 24% (01:58) wrong based on 55 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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Joined: 25 Feb 2013
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In the given figure, ABCD is a rectangle. P and Q are midpoints [#permalink]

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14 Oct 2017, 23:13
1
KUDOS
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
Intern
Joined: 28 Dec 2010
Posts: 49
Re: In the given figure, ABCD is a rectangle. P and Q are midpoints [#permalink]

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15 Oct 2017, 00:23
2
KUDOS
A more simpler way would be to assume it a square of side 1.
(Since square is also a rectangle with length = breadth)

$$= 1/4 + 1/4 + 1/8$$
$$= 5/8$$

$$= 3/8$$

Ratio: 5/3
C.
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Intern
Joined: 11 Apr 2017
Posts: 38
Schools: Kelley '20
Re: In the given figure, ABCD is a rectangle. P and Q are midpoints [#permalink]

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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.

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

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

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   [#permalink] 15 Oct 2017, 00:55
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