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In the figure above, square LMNO has a side of length 2x + 1 and the

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In the figure above, square LMNO has a side of length 2x + 1 and the  [#permalink]

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New post 11 Jan 2019, 01:47
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A
B
C
D
E

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  15% (low)

Question Stats:

96% (01:36) correct 4% (00:36) wrong based on 34 sessions

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In the figure above, square LMNO has a side of length 2x + 1 and the two smaller squares have sides of lengths 3 and 6. If the area of the shaded region is 76, what is the value of x?


A. 5
B. 6
C. 7
D. 11
E. 14

Attachment:
2019-01-11_1245.png
2019-01-11_1245.png [ 11.7 KiB | Viewed 357 times ]

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Re: In the figure above, square LMNO has a side of length 2x + 1 and the  [#permalink]

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New post 11 Jan 2019, 01:59
OA is A

Area of Big square- sum of area of smaller squares=76

(2x+1)^2-45=76
when we solve we get the roots of the equation -6,5 so the answer is A.

Bunuel wrote:
Image
In the figure above, square LMNO has a side of length 2x + 1 and the two smaller squares have sides of lengths 3 and 6. If the area of the shaded region is 76, what is the value of x?


A. 5
B. 6
C. 7
D. 11
E. 14

Attachment:
2019-01-11_1245.png

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Re: In the figure above, square LMNO has a side of length 2x + 1 and the  [#permalink]

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New post 11 Jan 2019, 04:30
Bunuel wrote:
Image
In the figure above, square LMNO has a side of length 2x + 1 and the two smaller squares have sides of lengths 3 and 6. If the area of the shaded region is 76, what is the value of x?


A. 5
B. 6
C. 7
D. 11
E. 14

Attachment:
2019-01-11_1245.png



(2x+1)^2 -45 = 76
solve for x
x= 5 & -6
IMO A
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Re: In the figure above, square LMNO has a side of length 2x + 1 and the  [#permalink]

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New post 11 Jan 2019, 12:18
Area of square LMNO= (2x+1)^2
Sum of Area of small squares= 3^2 + 6^2=9+36=45

Now, (2x+1)^2 -45=76 (area of shaded portion)
Thus (x+6)(x-5)=0
Hence, x=5
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Re: In the figure above, square LMNO has a side of length 2x + 1 and the   [#permalink] 11 Jan 2019, 12:18
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In the figure above, square LMNO has a side of length 2x + 1 and the

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