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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A$${w}^{2}+pw+k=0$$
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B$${w}^{2}-pw-2k=0$$
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C$${2}{w}^{2}+pw+2k=0$$
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D$${2}{w}^{2}-pw-2k=0$$
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E$${2}{w}^{2}-pw+2k=0$$
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正确答案: E