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02 Jun 2013, 08:13
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
74% (02:06) correct
26%
(02:03)
wrong
based on 181
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If the rectangular screen of a computer monitor is designed to have a length of x inches, a perimeter of P inches and an area of A square inches, which of these equations must be true?
A x^2 + Px + A = 0
B x^2 - Px - 2A = 0
C 2x^2 + Px + 2A = 0
D 2x^2 - Px - 2A = 0
E 2x^2 - Px + 2A = 0
Please explain!
A x^2 + Px + A = 0
B x^2 - Px - 2A = 0
C 2x^2 + Px + 2A = 0
D 2x^2 - Px - 2A = 0
E 2x^2 - Px + 2A = 0
Please explain!
02 Jun 2013, 08:19
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fozzzy
If one side is \(x\), lets call the other \(y\).
The \(P=2(x+y)\) and the \(A=xy\).
With those info the only equation that is true is E:
\(2x^2-x*2(x+y)+2xy=2x^2-2x^2-2xy+2xy=0\)
Hope it's clear
02 Jun 2013, 09:34
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fozzzy
Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.
Now, assume:
Length = x = 1 inch and width = 1 inch;
Perimeter = P = 4 inches;
Area = A = 1 square inches.
Plug the values of x, P, and A into the answer choices: only for E 2x^2 - Px + 2A = 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.
Hope it helps.
