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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]

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12 Jul 2006, 06:15
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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.

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12 Jul 2006, 06:40
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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12 Jul 2006, 10:01
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

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13 Jul 2006, 01:15
It is A indeed.

Thank you guys.
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13 Jul 2006, 01:23
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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13 Jul 2006, 01:31
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
13 Jul 2006, 01:31
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