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A rectangular garden has a perimeter of 560 feet. If the

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Manager
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A rectangular garden has a perimeter of 560 feet. If the [#permalink] New post 12 Jul 2006, 05:15
A rectangular garden has a perimeter of 560 feet. If the garden has a diagonal fence of 200 feet, what is the area of the garden, in square feet?

A) 19,200
B) 19'600
C) 20'000
D) 20'400
E) It cannot be calculated with the information given.

Please explain.
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 [#permalink] New post 12 Jul 2006, 05:40
You know that a+b=280, c=200 , a^2+2ab+b^2=280^2, use pitagoras to see that a^2+b^2=40000 2ab=38 400 and area is 19 200
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 [#permalink] New post 12 Jul 2006, 09:01
A) 19,200


Given 2(l+w) = 560 => (l+w) = 280

Diagonal = 200

i.e. 200 x 200 = l^2 + w^2

i.e 200x200 = (l+w)^2 - 2lw

i.e. 280x280 - 200x200 = 2lw

i.e 480 x 80 /2 = lw

i.e. 19,200 = lw

Answer : A
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 [#permalink] New post 13 Jul 2006, 00:15
It is A indeed.

Thank you guys.
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 [#permalink] New post 13 Jul 2006, 00:23
Let one side of the rectangle be x ft

The other side will be (560-2x)/2 = 280-x ft

So x^2 + (280-x)^2 = 200^2

x^2 + 280^2 - 560x + x^2 = 200^2
2x^2 - 560x + 38400 = 0
x^2 - 280x + 19200 = 0

x = 140 +/- 20 --> x can be 120 or 160

If x = 120, the other side = 160 --> Area = 19200
If x = 160, the other side = 120 --> Area = 19200

So both gives us an area of 19200

Ans A
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 [#permalink] New post 13 Jul 2006, 00:31
A 19200

Perimeter = 560
2(l+b) = 560
l+b = 280
(l+b)^2 = 280^2
l^2 + b^2 + 2lb = 280^2

Also diagonal = 200
l^2 + b^2 = 200^2

Substituting

280^2 - 2lb = 200^2
280^2 - 200^2 = 2lb
Lb = 19200
  [#permalink] 13 Jul 2006, 00:31
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A rectangular garden has a perimeter of 560 feet. If the

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