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A rectangular circuit board is designed to have perimeter p, diagonal

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A rectangular circuit board is designed to have perimeter p, diagonal  [#permalink]

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New post 11 Sep 2018, 02:50
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A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

71% (01:43) correct 29% (02:28) wrong based on 21 sessions

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A rectangular circuit board is designed to have perimeter p, diagonal  [#permalink]

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New post 11 Sep 2018, 05:17
Bunuel wrote:
A rectangular circuit board is designed to have perimeter p, diagonal d and area k. Which of the following equations must be true?


A. \(d^2 - p2 + 2k = 0\)

B. \(2d^2 - p2 + 2k = 0\)

C. \(4d^2 - p2 + 4k = 0\)

D. \(4d^2 - p2 + 8k = 0\)

E. \(4d^2 -2p2 + 8k = 0\)


Let, l and b be the dimensions of rectangle

Area = \(l*b = k\)
Perimeter \(= 2(l+b) = p\)
i.e. \((l+b) = p/2\)
Diagonal = \(√(l^2+b^2) = d\)
i.e. \((l^2+b^2) = d^2\)

Now, \((l+b)^2 = l^2+b^2 +2*l*b\)
i.e. \((p/2)^2 = d^2 +2*k\)

i.e. \((p)^2 = 4d^2 +8*k\)

i.e. \(4d^2 - p^2 + 8k = 0\)

Answer: Option D
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Re: A rectangular circuit board is designed to have perimeter p, diagonal  [#permalink]

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New post 14 Sep 2018, 17:52
Bunuel wrote:
A rectangular circuit board is designed to have perimeter p, diagonal d and area k. Which of the following equations must be true?


A. \(d^2 - p2 + 2k = 0\)

B. \(2d^2 - p2 + 2k = 0\)

C. \(4d^2 - p2 + 4k = 0\)

D. \(4d^2 - p2 + 8k = 0\)

E. \(4d^2 -2p2 + 8k = 0\)


(Note: p2 should be p^2.)

Let the length and width of the rectangular circuit board be L and W, respectively. So we have

2(L + W) = p, L^2 + W^2 = d^2 and LW = k

Since L + W = p/2, we have

(L + W)^2 = (p/2)^2

L^2 + W^2 + 2LW = p^2/4

Since L^2 + W^2 = d^2 and LW = k, we have:

d^2 + 2k = p^2/4

4d^2 + 8k = p^2

4d^2 + 8k - p^2 = 0

Answer: D
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Re: A rectangular circuit board is designed to have perimeter p, diagonal   [#permalink] 14 Sep 2018, 17:52
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