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If 7/11, 73/8, and q^2 are sides of a triangle and q is an integer, wh

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If 7/11, 73/8, and q^2 are sides of a triangle and q is an integer, wh  [#permalink]

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New post 06 Sep 2018, 00:35
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Re: If 7/11, 73/8, and q^2 are sides of a triangle and q is an integer, wh  [#permalink]

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New post 06 Sep 2018, 01:05
Bunuel wrote:
If 7/11, 73/8, and q^2 are sides of a triangle and q is an integer, what is q?

A. 6
B. 5
C. 4
D. 3
E. 2



Use The triangle inequality rule : the length of a side of a triangle is less than the sum of the lengths of the other two sides and greater than the difference of the lengths of the other two sides.

the length of a side of a triangle is less than the sum of the lengths of the other two sides
so \(q^2<\frac{7}{11}+\frac{73}{8}........~.q^2<9+1.....or.....q^2<\frac{859}{88}........q^2<10.......q<4\)
\(q^2>\frac{73}{8}-\frac{7}{11}......q^2>9-1.............q^2>8......q>2\)


Only possibility is 3

D
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Re: If 7/11, 73/8, and q^2 are sides of a triangle and q is an integer, wh  [#permalink]

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New post 06 Sep 2018, 08:36
Bunuel wrote:
If 7/11, 73/8, and q^2 are sides of a triangle and q is an integer, what is q?

A. 6
B. 5
C. 4
D. 3
E. 2


7/11 ~ 0.6
73/8 ~ 9.1
The sum of any two sides of a triangle is greater than the third side and the difference of any two sides is lesser than the third side.
\(q^2\) cannot be equal to 1,4.
If \(q^2\)=9, sum of any two sides > third side, similarly, difference of any two sides < third side.
q=3
Answer D.
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Re: If 7/11, 73/8, and q^2 are sides of a triangle and q is an integer, wh &nbs [#permalink] 06 Sep 2018, 08:36
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