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# Two goats are each tied at corners A and B of a fenced rectangular fie

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Math Expert
Joined: 02 Sep 2009
Posts: 59095
Two goats are each tied at corners A and B of a fenced rectangular fie  [#permalink]

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22 Oct 2019, 22:34
00:00

Difficulty:

25% (medium)

Question Stats:

86% (02:00) correct 14% (02:46) wrong based on 22 sessions

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Two goats are each tied at corners A and B of a fenced rectangular field of area 50. The goat's tethers allow them to graze within circular regions of radius 5, centered at A and B, respectively. The two grazing areas meet at point G, but do not overlap. If the goats graze the entire shaded area within their respective reach by the end of the day, what is the area of the un-grazed, un-shaded region?

A. 50 - 25∏

B. 25(2 - ∏/2)

C. 25(2 - ∏/4)

D. 12.5 ∏

E. 25∏

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T1000.png [ 6.3 KiB | Viewed 227 times ]

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Two goats are each tied at corners A and B of a fenced rectangular fie  [#permalink]

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22 Oct 2019, 23:36
1
According to question

AG=BG=5

Area of ABCD= 50
Area of un-shaded region= Area of ABCD - Area of two quarter of circle with radius 5

=>Area of un-shaded region= 50 - ($$\frac{∏* 5^2}{4}$$ + $$\frac{∏* 5^2}{4}$$)

=50 - $$\frac{25∏}{2}$$

=25(2- ∏/2) (B) Ans
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Re: Two goats are each tied at corners A and B of a fenced rectangular fie  [#permalink]

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22 Oct 2019, 23:40
area grazed
2*90/360*pi*25 ;25pi/2
total area; 50
left area ;
50-25pi/2 or say
25(2 - ∏/2)
IMO B

Bunuel wrote:

Two goats are each tied at corners A and B of a fenced rectangular field of area 50. The goat's tethers allow them to graze within circular regions of radius 5, centered at A and B, respectively. The two grazing areas meet at point G, but do not overlap. If the goats graze the entire shaded area within their respective reach by the end of the day, what is the area of the un-grazed, un-shaded region?

A. 50 - 25∏

B. 25(2 - ∏/2)

C. 25(2 - ∏/4)

D. 12.5 ∏

E. 25∏

Attachment:
T1000.png
Re: Two goats are each tied at corners A and B of a fenced rectangular fie   [#permalink] 22 Oct 2019, 23:40
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