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What is the area of a rectangular garden with diagonal

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What is the area of a rectangular garden with diagonal [#permalink]

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New post 23 Feb 2012, 13:21
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What is the area of a rectangular garden with diagonal length of 200 feet and a perimeter of 560 feet?

Hi everybody,

I am stuck with the following problem. Would be great if someone could give me the answer.

What is the area of a rectangular garden with diagonal length of 200 feet and a perimeter of 560 feet?

The answer is 19200 but I dont get it.

Many thanks in advance!!!
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Re: What is the area of a rectangular garden with diagonal [#permalink]

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New post 23 Feb 2012, 13:36
What is the area of a rectangular garden with diagonal length of 200 feet and a perimeter of 560 feet?

Let the sides of a rectangular garden be \(x\) and \(y\).

Given: \(Diagonal^2=x^2+y^2=200^2\) and \(Perimeter=2(x+y)=560\) --> \(x+y=280\).
Question: \(Area=xy=?\)

Square \(x+y=280\): \(x^2+2xy+y^2=280^2\);

Substitute \(x^2+y^2\): \(2xy+200^2=280^2\) --> \(2xy=280^2-200^2\);

Apply \(a^2-b^2=(a-b)(a+b)\): \(2xy=(280-200)(280+200)=80*480\) --> \(xy=80*240=19,200\).

Hope it's clear.

P.S. Please post answer choices for PS questions when available.
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Joined: 09 Feb 2012
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Re: What is the area of a rectangular garden with diagonal [#permalink]

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New post 25 Feb 2012, 09:08
Super! Many thanks for your help. Totally clear now!

Unfortunately there were not answer choices. It was an open question.
Re: What is the area of a rectangular garden with diagonal   [#permalink] 25 Feb 2012, 09:08
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