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Which is greater x or 90

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sandy
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Which is greater x or 90 [#permalink] New post   26 Sep 2018, 14:59
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Quantity A
Quantity B
\(x\)
\(90\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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A
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GreenlightTestPrep
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Re: x vs 90 [#permalink] New post   01 Oct 2018, 10:36
1
sandy wrote:
Attachment:
Capture.JPG


Quantity A
Quantity B
x
90


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


First notice that IF the measurements were 6, 8, 10, then we'd have a RIGHT TRIANGLE
Image
In this case, x = 90 degrees

HOWEVER, we want the 3rd side to have length 10.5 (while keeping the other 2 lengths of 6 and 8)
To increase the 3rd side from a length of 10 to a length of 10.5, just "grab" the 2 vertices (shown below) and pull them apart.
Image
When we do this, the 90-degree angle OPENS UP to be greater than 90 degrees.

In other words, x > 90

Answer: A

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Brent
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Re: x vs 90 [#permalink] New post   13 Dec 2019, 11:32
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In this case, if x was 90 the side opposite to it (hypotenuse) is 10 . If the angle opposite to 10 is 90 then what would the angle opposite to 10.5. Definitely greater that 90 based on the fact "In a triangle, the larger the angle opposite to side, the larger the side."
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Re: Which is greater x or 90 [#permalink] New post   21 Dec 2019, 21:25
if this was a 30 60 90 triangle the hypotenuse would have been 10. Since it is more than 10. the angle in this case X would be more than 90
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Re: Which is greater x or 90 [#permalink]
21 Dec 2019, 21:25
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