A larger playground has a rectangular-shaped track shaded shown as abo

Question

Square.jpg 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.

nikhiljd · Answer

The Ans: C
1 and 2 give partial info .
1+2: 
d=20
Area = 20*8*20=3200

paidlukkha · Answer

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

nikhiljd · Answer

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

paidlukkha · Answer

nikhiljd  still not clear :'(
 MathRevolution  please post the official solution

MathRevolution · Answer

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 [ 4.53 KiB | Viewed 2468 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.

bumpbot · Answer

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A larger playground has a rectangular-shaped track shaded shown as abo

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