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, 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]

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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Intern

Joined: 09 Feb 2012

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

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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What is the area of a rectangular garden with diagonal

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What is the area of a rectangular garden with diagonal

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