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655-705 (Hard)|   Geometry|      
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MathRevolution
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A larger playground has a rectangular-shaped track shaded shown as abo 07 Apr 2016, 06:11
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C
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65% (hard)

Question Stats:

52% (02:26) correct 48% (02:08) wrong based on 87 sessions

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A larger playground has a rectangular-shaped track shaded shown as above figure such that the track has a uniform d as its width, what is the track’s area?

1) The perimeter of smaller playground is 18d.
2) The perimeter of smaller playground is 360.


* A solution will be posted in two days.
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C
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A larger playground has a rectangular-shaped track shaded shown as abo 17 Apr 2016, 08:45
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The Ans: C
1 and 2 give partial info .
1+2:
d=20
Area = 20*8*20=3200
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A larger playground has a rectangular-shaped track shaded shown as abo 17 Apr 2016, 10:02
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I got why ABD are out but when it came to C & E
I got d=20..so far so good...

nikhiljd how you landed up in this Area = 20*8*20=3200
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A larger playground has a rectangular-shaped track shaded shown as abo 17 Apr 2016, 12:27
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It will sound weird...
The entire shade region if unfolded will be one long rectangle .
the width =d ,and the lengths = to the remaining of 18d-2d =16d ..
Since it is a rectangle each length is now 8d ,so area = l*b=8d * d =8*20*20
or as in my original post 20*8*20...
I hope I am clear.. I am not so good explaining ...but if you want more explanation I will try
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A larger playground has a rectangular-shaped track shaded shown as abo 19 Apr 2016, 12:06
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nikhiljd still not clear :'(
MathRevolution please post the official solution
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A larger playground has a rectangular-shaped track shaded shown as abo 21 Apr 2016, 01:13
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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A larger playground has a rectangular-shaped track shaded shown as above figure such that the track has a uniform d as its width, what is the track’s area?

1) The perimeter of smaller playground is 18d.
2) The perimeter of smaller playground is 360.
Attachment:
square.jpg
square.jpg [ 4.53 KiB | Viewed 2382 times ]

Just like the picture above, suppose width and height as a and b respectively. Then, the area of the track is (a+2d)(b+2d)-ab=(a+b)2d+4d^2 and there are 3 varaibles(a,b,c). In order to match with the number of equations, you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), from 2(a+b)=18d=360, a+b=180 and d=2 are derived, which is unique and sufficient.
Thus, the answer is C.
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A larger playground has a rectangular-shaped track shaded shown as abo 13 Jan 2022, 08:03
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