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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]  23 Feb 2012, 12:21
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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.

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Re: What is the area of a rectangular garden with diagonal [#permalink]  23 Feb 2012, 12:36
Expert's post
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.

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Re: What is the area of a rectangular garden with diagonal [#permalink]  25 Feb 2012, 08:08
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, 08:08
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