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# The figure above represents a rectangular plot of land that is to be d

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Math Expert
Joined: 02 Sep 2009
Posts: 58378
The figure above represents a rectangular plot of land that is to be d  [#permalink]

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11 Sep 2018, 02:36
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Difficulty:

55% (hard)

Question Stats:

44% (01:37) correct 56% (01:15) wrong based on 32 sessions

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The figure above represents a rectangular plot of land that is to be divided diagonally between two farmers with a fence. If the fence is to go from one corner to a corner diagonal, how long is the fence going to be?

(1) The area of the entire plot of land is 563 square meters.
(2) The square of the sum of the length and width of the plot is 2890.

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image008.jpg [ 1.11 KiB | Viewed 574 times ]

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Re: The figure above represents a rectangular plot of land that is to be d  [#permalink]

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11 Sep 2018, 05:24
Bunuel wrote:

The figure above represents a rectangular plot of land that is to be divided diagonally between two farmers with a fence. If the fence is to go from one corner to a corner diagonal, how long is the fence going to be?

(1) The area of the entire plot of land is 563 square meters.
(2) The square of the sum of the length and width of the plot is 2890.

Attachment:
image008.jpg

Question : Length of Fence =Diagonal fo the rectangle $$= √(l^2+b^2) = ?$$

Statement 1:The area of the entire plot of land is 563 square meters.
i.e. l*b = 563
NOT SUFFICIENT

Statement 2:The square of the sum of the length and width of the plot is 2890.
i.e. $$(l^2+b^2) = 2890$$
i.e. Diagonal $$= √2890$$
SUFFICIENT

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Re: The figure above represents a rectangular plot of land that is to be d  [#permalink]

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30 Sep 2018, 02:25
Let x be the length and y be the breadthof the rectgangle. Asked = x+y+sqrt(x^2+y^2)
1. xy = 563 . Not sufficient
2. x^2+y^2 = 2890 or sqrt(x^+y^2) =sqrt(2890)

1+2------> multiply 1 by 2 we get, 2xy = 563*2
we get x^2 + y^2 + 2xy = 2890 + 1126
or (x+y)^2 = smthng
or x+y = sqrt (some real no )= some real no
Thus, combination is sufficient
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Re: The figure above represents a rectangular plot of land that is to be d   [#permalink] 30 Sep 2018, 02:25
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