Bunuel wrote:
Which of the following expresses the perimeter of a square region in terms of its area K?
(A) 4K
(B) 2√K
(C) √(2K)
(D) 4√K
(E) 4K√K
AlgebraFor perimeter P*:
\(A_{square} = (\frac{P}{4})^2\)\(A = \frac{P^{2}}{4^{2}}\)\(A = \frac{P^{2}}{16}\)\(16A = P^2\) , substitute
\(K\) for
\(A\) (
\(A = K\))
\(P^2 = 16K\)\(P = \sqrt{16K}\) \(P = 4\sqrt{K}\)Answer D*The initial formula is easily derived, where side of square = s
s * 4 = P
s = \(\frac{P}{4}\)
Area = s * s = \((\frac{P}{4}) * (\frac{P}{4})\)
Area = \((\frac{P}{4})^2\)
Choose numbersLet side
s = 2
P = 4s = 8
A = K = s\(^2\) = 4
Perimeter in terms of square's area K?
P = 8, K = 4(A) 4K? INCORRECT. 4K = 16, and
\(16\neq{8}\) (B) 2√K? INCORRECT. 2√K = (2*2) = 4, and
\(4\neq{8}\)(C) √(2K)? INCORRECT. √(2K) = √(8), and
\(√8 \neq{8}\)(D) 4√K? CORRECT. 4√K =
\((4 * 2) = 8\) (E) 4K√K? INCORRECT. 4K√K = 16 * 2 = 32, and
\(32\neq{8}\)Answer D _________________
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