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# A piece of metal wire 20 meters long is cut into two pieces. One piece

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Math Expert
Joined: 02 Sep 2009
Posts: 50570
A piece of metal wire 20 meters long is cut into two pieces. One piece  [#permalink]

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16 Oct 2018, 00:38
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Difficulty:

45% (medium)

Question Stats:

69% (01:29) correct 31% (02:01) wrong based on 39 sessions

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A piece of metal wire 20 meters long is cut into two pieces. One piece is used to form a circle with radius r , and the other is used to form a square. Which of the following represents the area of the square, in square meters?

(A) (5 − 1/4*πr^2)

(B) (5 − 2πr)^2

(C) 1/4*π^2*r^2

(D) (10 − 2πr)^2

(E) (5 − 1/2*πr)^2

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Re: A piece of metal wire 20 meters long is cut into two pieces. One piece  [#permalink]

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16 Oct 2018, 00:47
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Length of the wire, 20 = circumference of the circle + Perimeter of the square.

20 = 2πr + 4a (a is the side of the square)

10 = πr + 2a

a = 5 - $$\frac{πr}{2}$$

Area of the square = $$a^2$$ = $$(5 - \frac{πr}{2})^2$$

Bunuel, Last option might be wrong. can you check.?

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Re: A piece of metal wire 20 meters long is cut into two pieces. One piece  [#permalink]

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16 Oct 2018, 00:50
Afc0892 wrote:
Length of the wire, 20 = circumference of the circle + Perimeter of the square.

20 = 2πr + 4a (a is the side of the square)

10 = πr + 2a

a = 5 - $$\frac{πr}{2}$$

Area of the square = $$a^2$$ = $$(5 - \frac{πr}{2})^2$$

Bunuel, Last option might be wrong. can you check.?

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Edited. Thank you.
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Re: A piece of metal wire 20 meters long is cut into two pieces. One piece  [#permalink]

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26 Oct 2018, 12:53
The circle has a circumference of 2πr, hence the side of the square is going to be 20 - 2πr.

Area of square is equal to (20 - 2πr)^2. Only answer E satisfies this.
Re: A piece of metal wire 20 meters long is cut into two pieces. One piece &nbs [#permalink] 26 Oct 2018, 12:53
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