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What is the area of a square that has a diagonal of length 10?

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gmatpapa
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What is the area of a square that has a diagonal of length 10? [#permalink] New post   03 Feb 2011, 08:43
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What is the area of a square that has a diagonal of length 10?

A. 5
B. 10
C. 20
D. 40
E. 45

Source: Cliff's GMAT

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Re: What is the area of a square that has a diagonal of length 10? [#permalink] New post   03 Feb 2011, 08:54
Expert Reply
gmatpapa wrote:
What is the area of a square that has a diagonal of length 10?

A. 5
B. 10
C. 20
D. 40
E. 45

Source: Cliff's GMAT


\(area_{square}=side^2=\frac{diagonal^2}{2}\): so A to be the answer either option A should read 50 instead of 5 or diagonal should be \(\sqrt{10}\) instead of 10.
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Re: What is the area of a square that has a diagonal of length 10? [#permalink] New post   03 Feb 2011, 09:02
Bunuel wrote:
gmatpapa wrote:
What is the area of a square that has a diagonal of length 10?

A. 5
B. 10
C. 20
D. 40
E. 45

Source: Cliff's GMAT


\(area_{square}=side^2=\frac{diagonal^2}{2}\): so A to be the answer either option A should read 50 instead of 5 or diagonal should be \(\sqrt{10}\) instead of 10.


Yes. Answer quite clearly should be 50.

Does this OE make sense to you:
From the relationship that exists in a right triangle, we see that the sides of the square
must equal the square root of 5. Thus the area of the square is 5
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Re: What is the area of a square that has a diagonal of length 10? [#permalink] New post   03 Feb 2011, 09:07
Expert Reply
gmatpapa wrote:
Bunuel wrote:
gmatpapa wrote:
What is the area of a square that has a diagonal of length 10?

A. 5
B. 10
C. 20
D. 40
E. 45

Source: Cliff's GMAT


\(area_{square}=side^2=\frac{diagonal^2}{2}\): so A to be the answer either option A should read 50 instead of 5 or diagonal should be \(\sqrt{10}\) instead of 10.


Yes. Answer quite clearly should be 50.

Does this OE make sense to you:
From the relationship that exists in a right triangle, we see that the sides of the square
must equal the square root of 5. Thus the area of the square is 5


As OE says that \(side=\sqrt{5}\) then there must be the second case I suggested: diagonal should be \(\sqrt{10}\) instead of 10.
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Re: What is the area of a square that has a diagonal of length 10? [#permalink] New post   03 Feb 2011, 09:15
Yep. Quite correct as diagonal = \(sqrt2\)*side. So side will be \(\frac{sqrt10}{sqrt2}\)= \(sqrt 5\). And area will be \(side^2= 5\).
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Re: What is the area of a square that has a diagonal of length 10? [#permalink] New post   05 Feb 2011, 05:03
i did a bit different - x^2+x^2 = 10^2
x=squrt2*5
x^2 = 2*25 = 50
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gmatpapa
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Re: What is the area of a square that has a diagonal of length 10? [#permalink] New post   05 Feb 2011, 06:01
144144 wrote:
i did a bit different - x^2+x^2 = 10^2
x=squrt2*5
x^2 = 2*25 = 50


Its essentially the same thing if you look at it. Diagonal= \(sqrt2\)*side is arrived using the same formula that you have used. (Pythagoras theorem)
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Re: What is the area of a square that has a diagonal of length 10? [#permalink] New post   05 Feb 2011, 10:23
ye, i noticed it after i posted. thanks.

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This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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Re: What is the area of a square that has a diagonal of length 10? [#permalink]
05 Feb 2011, 10:23
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