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The area of the triangular region

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The area of the triangular region [#permalink] New post 17 Jun 2018, 13:33
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Question Stats:

75% (01:06) correct 25% (00:48) wrong based on 12 sessions
Attachment:
triangle.jpg
triangle.jpg [ 6.88 KiB | Viewed 389 times ]


Quantity A
Quantity B
The area of the triangular region
25


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: The area of the triangular region [#permalink] New post 18 Jun 2018, 20:55
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From the figure we know that this is a 45-45-90 triangle.
In a 45-45-90 triangle sides are distributed with length that it is \(x-x-x\sqrt{2}\)
Given the side with length 10 is opposite to the 90 degree angle.
\(x\sqrt{2} = 10\)
Therefore, \(x = 10/\sqrt{2}\)
\(x = 2*5/\sqrt{2}\)
\(x = 5\sqrt{2}\)
Since this is an isosceles right triangle with height = base = x = \(5\sqrt{2}\)
we can get the area of a triangle as \(\frac{1}{2}* base * height\)
area = \(\frac{1}{2} * 5\sqrt{2}* 5\sqrt{2} = 25\)
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Re: The area of the triangular region   [#permalink] 18 Jun 2018, 20:55
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The area of the triangular region

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