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If in a right-angled triangle, the ratio of the longer leg t
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honchos
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If in a right-angled triangle, the ratio of the longer leg t [#permalink] New post  06 Mar 2014, 22:26
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If in a right-angled triangle, the ratio of the longer leg to the shorter is √2:1, what is the ratio of the shorter leg to the hypotenuse?

A. 1:3
B. 1:√3
C. √2:√3
D. 3:2
E. √3:1

Doubt: Actually the question is pretty straightforward but "leg" is used only for base and height? or we can use the word in question stem for any of the 3 components that makes up for a right angled triangle: Hypotenuse, base, Height.

M23-03
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Bunuel
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Re: If in a right-angled triangle, the ratio of the longer leg t [#permalink] New post  07 Mar 2014, 01:22
Expert Reply
honchos wrote:
If in a right-angled triangle, the ratio of the longer leg to the shorter is √2:1, what is the ratio of the shorter leg to the hypotenuse?

1:3
1:√3
√2:√3
3:2
√3:1

Doubt: Actually the question is pretty straightforward but "leg" is used only for base and height? or we can use the word in question stem for any of the 3 components that makes up for a right angled triangle: Hypotenuse, base, Height.


In a right triangle the sides adjacent to the right angle are called legs (or catheti, singular: cathetus).

Can you please tell me the ID (M?-?) of this question in GMAT Club's test?
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honchos
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Re: If in a right-angled triangle, the ratio of the longer leg t [#permalink] New post  07 Mar 2014, 01:26
Bunuel wrote:
honchos wrote:
If in a right-angled triangle, the ratio of the longer leg to the shorter is √2:1, what is the ratio of the shorter leg to the hypotenuse?

1:3
1:√3
√2:√3
3:2
√3:1

Doubt: Actually the question is pretty straightforward but "leg" is used only for base and height? or we can use the word in question stem for any of the 3 components that makes up for a right angled triangle: Hypotenuse, base, Height.


In a right triangle the sides adjacent to the right angle are called legs (or catheti, singular: cathetus).

Can you please tell me the ID (M?-?) of this question in GMAT Club's test?


Bunuel,

This is the ID-
Quantitative :: Problem solving :: Geometry :: M23-03
http://screencast.com/t/sSoAzL1fpbA
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Bunuel
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Re: If in a right-angled triangle, the ratio of the longer leg t [#permalink] New post  07 Mar 2014, 01:30
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honchos wrote:
Bunuel wrote:
honchos wrote:
If in a right-angled triangle, the ratio of the longer leg to the shorter is √2:1, what is the ratio of the shorter leg to the hypotenuse?

1:3
1:√3
√2:√3
3:2
√3:1

Doubt: Actually the question is pretty straightforward but "leg" is used only for base and height? or we can use the word in question stem for any of the 3 components that makes up for a right angled triangle: Hypotenuse, base, Height.


In a right triangle the sides adjacent to the right angle are called legs (or catheti, singular: cathetus).

Can you please tell me the ID (M?-?) of this question in GMAT Club's test?


Bunuel,

This is the ID-
Quantitative :: Problem solving :: Geometry :: M23-03
http://screencast.com/t/sSoAzL1fpbA


Thank you very much!
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Abhishek009
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Re: If in a right-angled triangle, the ratio of the longer leg t [#permalink] New post  09 May 2016, 07:57
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Kudos
honchos wrote:
If in a right-angled triangle, the ratio of the longer leg to the shorter is √2:1, what is the ratio of the shorter leg to the hypotenuse?

A. 1:3
B. 1:√3
C. √2:√3
D. 3:2
E. √3:1

Doubt: Actually the question is pretty straightforward but "leg" is used only for base and height? or we can use the word in question stem for any of the 3 components that makes up for a right angled triangle: Hypotenuse, base, Height.

M23-03


Attachment:
Untitled.png
Untitled.png [ 4.34 KiB | Viewed 1443 times ]


Since the is a right angled triangle

\({AC}^2\) = \({AB}^2\) + \({BC}^2\)

So, \({AC}^2\) = \({√2}^2\) + \({1}^2\)

Or, \({AC}^2\) = \({2}\) + \({1}\)

Or, \(AC\) = √3

Quote:
Ratio of the shorter leg to the hypotenuse


Will be \(\frac{BC}{AC}\) => 1:√3

Hence answer will be (B)
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Re: If in a right-angled triangle, the ratio of the longer leg t [#permalink] New post  03 Jun 2018, 00:21
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