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A rectangular circuit board is designed to have width w inch [#permalink]

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14 Jun 2005, 07:55

6

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A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

67% (02:30) correct
33% (01:49) wrong based on 853 sessions

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A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

. Hello need help thanks A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true? (A) w^2+pw+k=0 (B) w^2-pw+2k=0 (C) 2 w^2+pw+2k=0 (D) 2 w^2-pw-2k=0 (E) 2w^2-pw+2k=0

. Hello need help thanks A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true? (A) w^2+pw+k=0 (B) w^2-pw+2k=0 (C) 2 w^2+pw+2k=0 (D) 2 w^2-pw-2k=0 (E) 2w^2-pw+2k=0

Another way to solve the problem is to choose a rectangle of your own.

I chose one , in which each side was 1 unit.
hence w =1 , p =4 and k = 1.

. Hello need help thanks A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true? (A) w^2+pw+k=0 (B) w^2-pw+2k=0 (C) 2 w^2+pw+2k=0 (D) 2 w^2-pw-2k=0 (E) 2w^2-pw+2k=0

Let l be the length of the board, then p = 2l + 2w, k = w*l By plugging, we can find that the answer is E: \(2w^2 - w(2l + 2w) + 2w*l = 0\), thus 2w - 2l - 2w + 2l = 0

A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.

Now, assume: Width = w = 1 inch and length = 1 inch; Perimeter = p = 4 inches; Area = k = 1 square inches.

Plug the values of w, p, and k into the answer choices: only for E 2w^2 - pw + 2k = 2 - 4 + 2 = 0.

Answer: E.

Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only.

Re: A rectangular circuit board is designed to have width w inch [#permalink]

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25 Jul 2013, 03:47

In order to solve this problem algebraicaly we need the following formulaes:

\(Perimeter = 2*w + 2*h\) \(Area = w * h\)

We begin by observing what information we have. The left-hand side in both of the above formulae is known, and defined as p and k. We also have the width, w. We can then use what we know to find the height, by rearranging terms:

\(p= 2*w + 2*h\) ===> \(h = \frac{p-2*w}{2}\).

Slot this into the formulae for the area to obtain

Re: A rectangular circuit board is designed to have width w inch [#permalink]

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25 Jul 2013, 20:10

For a rectangle, if one side = w & perimeter = p, then the other side is (p-2w)/2 So, area k = w x (p-2w)/2 Solving the above, we get answer = E (2w^2 - pw + 2k = 0)
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Re: A rectangular circuit board is designed to have width w inch [#permalink]

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19 Nov 2013, 06:24

mandy wrote:

A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

Start by E always on these types of questions. E is the correct answer choice.

And also try to use different numbers just in case. Here we used different numbers for length and width Needless to say try to avoid 0,1, or any negative numbers

Re: A rectangular circuit board is designed to have width w inch [#permalink]

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16 May 2014, 02:35

mandy wrote:

A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

I supposed the rectangle to be a square and w = 1 , then P = 4 and k = 1 (A) & (C) always positive so we can safely eliminate those choices and a quick calculation allows to eliminate (B) and (D) hence the correct answer is (E)

Re: A rectangular circuit board is designed to have width w inch [#permalink]

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16 Feb 2016, 10:21

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Re: A rectangular circuit board is designed to have width w inch [#permalink]

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09 Apr 2016, 09:24

mandy wrote:

A rectangular circuit board is designed to have width w inches, perimeter p inches, and area k square inches. Which of the following equations must be true?

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