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# Which of the following expresses the perimeter of a square region in

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Which of the following expresses the perimeter of a square region in [#permalink]
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

Algebra

For 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 $$A$$ ($$A = K$$)

$$P^2 = 16K$$

$$P = \sqrt{16K}$$

$$P = 4\sqrt{K}$$

*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 numbers

Let 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 $$32\neq{8}$$

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Which of the following expresses the perimeter of a square region in [#permalink]
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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

Area of square = (length of one side)²
We're told that the area of the square is K
So, (length of one side)² = K
Solve to get: (length of one side) = √K

Which of the following expresses the perimeter of a square region
Perimeter of a square = (4)(length of one side)
So, perimeter = (4)(√K)

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Re: Which of the following expresses the perimeter of a square region in [#permalink]
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Re: Which of the following expresses the perimeter of a square region in [#permalink]
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