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# A right triangle has a hypotenuse of 12 and legs of 9 and y.

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A right triangle has a hypotenuse of 12 and legs of 9 and y. [#permalink]  26 Sep 2018, 14:55
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94% (00:30) correct 5% (00:00) wrong based on 17 sessions
A right triangle has a hypotenuse of 12 and legs of 9 and y.

 Quantity A Quantity B y 15

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.
[Reveal] Spoiler: OA

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Sandy
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Re: A right triangle has a hypotenuse of 12 and legs of 9 and y. [#permalink]  22 Oct 2018, 23:12
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We are given that the triangle is a right-angled triangle.
Therefore, the sides follow the Pythagoras theorem
$$y^2 + 9^2 = 12^2$$
or, $$y^2 = 144-81$$
or $$y^2 = 63$$
or, $$y = 7.93$$
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Re: A right triangle has a hypotenuse of 12 and legs of 9 and y. [#permalink]  11 Jan 2019, 21:36
No need calculation. As hypotenuses hold highest value, Value of y should be less than hypotenuses. Hence B.
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Re: A right triangle has a hypotenuse of 12 and legs of 9 and y. [#permalink]  11 Jan 2019, 22:22
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Expert's post
sandy wrote:
A right triangle has a hypotenuse of 12 and legs of 9 and y.

 Quantity A Quantity B y 15

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.

Given that 12 is the hypotenuse, the largest side of the triangle will be 12.

so y will be less than 12, and hence 15>y..
B>A

B
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
3. Remainders : https://greprepclub.com/forum/remainders-what-you-should-know-11524.html
4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

Re: A right triangle has a hypotenuse of 12 and legs of 9 and y.   [#permalink] 11 Jan 2019, 22:22
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