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# A computer manufacturer claims that a perfectly square

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Intern
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A computer manufacturer claims that a perfectly square [#permalink]  26 Sep 2007, 14:15
A computer manufacturer claims that a perfectly square computer monitor has a diagonal size of 20 inches. However, part of the monitor is made up of a plastic frame surrounding the actual screen. The area of the screen is three times the size of that of the surrounding frame. What is the diagonal of the screen?
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Re: Geomtry [#permalink]  26 Sep 2007, 15:00
inwosu wrote:
A computer manufacturer claims that a perfectly square computer monitor has a diagonal size of 20 inches. However, part of the monitor is made up of a plastic frame surrounding the actual screen. The area of the screen is three times the size of that of the surrounding frame. What is the diagonal of the screen?

10*sqrt(6)

As = Screen Area
Am = Monitor Area
Af = Frame Area

Am = 200, therefore, Sm = 10*sqrt(2)

As = 3*Af = Af+As
2Af = As = 200
Af = 100

Therefore, As = 3*100 = 300
and Ss = 10*sqrt(3)

We know that the frame has width:
(10*sqrt(3) - 10*sqrt(2))/2 = 5*(sqrt(3) - sqrt(2))

Therefore, the corner of the monitor to the corner of the frame is:
sqrt(2)*5*(sqrt(3) - sqrt(2))

Total diameter of the frame:
Ans = 2*sqrt(2)*5*(sqrt(3) - sqrt(2)) + 20
= 10*sqrt(6) - 10*2 + 20
= 10*sqrt(6)
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The answer is sqrt of 300.
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inwosu wrote:
The answer is sqrt of 300.

If I understand the question correctly, this answer is impossible.
sqrt(300) = sqrt(10*10*3) = 10*sqrt(3) = 10*1.7 = 17

If the monitor has diameter of 20, it is impossible for the screen to have diameter of 17. The total diameter must be greater than 20. This is based on my understanding of the question. It is possible that I understand it incorrectly.
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bkk145 wrote:
If the monitor has diameter of 20, it is impossible for the screen to have diameter of 17. The total diameter must be greater than 20. This is based on my understanding of the question. It is possible that I understand it incorrectly.

You can verify in this way:
Monitor diagonal = 20 = 10 sqrt4; Monitor area = 400
Screen diagonal = 10 sqrt3; Screen area = 300
Frame area = 400-300 = 100 = 300/3 = 1/3 Screen area.
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I get 10sqrt6 as well...
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Re: Geomtry [#permalink]  26 Sep 2007, 19:13
inwosu wrote:
A computer manufacturer claims that a perfectly square computer monitor has a diagonal size of 20 inches. However, part of the monitor is made up of a plastic frame surrounding the actual screen. The area of the screen is three times the size of that of the surrounding frame. What is the diagonal of the screen?

I get sqrt of 300 as well.

Let Sc = area of screen computer, Sf= screen frame , St= total screen.

*The diagonal St is 20 inches.
*As we know that it is a square, the diagonal divides it in 2 perfect rectangle triangles: 45 - 45 - 90------> 20/2^(1/2) - 20/2^(1/2) - 20.

*20/2^(1/2) is the measure side of the total screen St and from that the total area (square) is 20/2^(1/2) * 20/2^(1/2)= 200 inches^2.

* St = Sc + Sf and Sc = 3 Sp
3 Sp + Sp = 200 ----->> Sp = 5o inches^2 and Sc= 150 inches^2.

* The ares Sc= 150 and the screen is square.
one side of the screen = 150^(1/2) and using Pythagore the diagonale is { [150^(1/2)]^2 + [150^(1/2)]^2 }^ 1/2 = 300 ^ (1/2)
Re: Geomtry   [#permalink] 26 Sep 2007, 19:13
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