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The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh

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The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh  [#permalink]

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New post 09 Aug 2018, 00:33
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[Math Revolution GMAT math practice question]

The lengths of two sides of a certain obtuse triangle are \(9\) and \(12\). Which of the following could be the length of the third side of the triangle?

\(A. 12\)
\(B. 13\)
\(C. 14\)
\(D. 15\)
\(E. 16\)

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Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh  [#permalink]

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New post 09 Aug 2018, 01:05
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The lengths of two sides of a certain obtuse triangle are \(9\) and \(12\). Which of the following could be the length of the third side of the triangle?

\(A. 12\)
\(B. 13\)
\(C. 14\)
\(D. 15\)
\(E. 16\)


OA: E
For obtuse angle
\(a^2+b^2<c^2\)
As answer options are greater than or equal to sides given in question stem i.e \(9,12\). \(c\) would be the dimension of the side opposite the obtuse angle.
\(a\) and \(b\) can be either \(9\) or \(12\).

\(a^2+b^2 = 9^2+12^2=81+144 =225\)

\(c^2\) can be found out by squaring the answer option
A) 144
B) 169
C) 196
D) 225
E) 256
Only Option E satisfies \(a^2+b^2<c^2\) i.e \(225< 256\)
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Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh  [#permalink]

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New post 09 Aug 2018, 08:19
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The lengths of two sides of a certain obtuse triangle are \(9\) and \(12\). Which of the following could be the length of the third side of the triangle?

\(A. 12\)
\(B. 13\)
\(C. 14\)
\(D. 15\)
\(E. 16\)


\(H = \sqrt{12^2 + 9^2}\)

Or, \(H = \sqrt{225}\)

So, \(H = 15\), Answer must be (D)
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Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh  [#permalink]

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New post 09 Aug 2018, 08:24
Abhishek009 wrote:
\(H = \sqrt{12^2 + 9^2}\)

Or, \(H = \sqrt{225}\)

So, \(H = 15\), Answer must be (D)

Abhishek009
I guess its c^2 > a^2 + b^2 for an obtuse triangle, and not c^2 = a^2 + b^2

Please correct me if I am wrong.
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Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh  [#permalink]

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New post 09 Aug 2018, 08:27
MathRevolution wrote:
[Math Revolution GMAT math practice question]

The lengths of two sides of a certain obtuse triangle are \(9\) and \(12\). Which of the following could be the length of the third side of the triangle?

\(A. 12\)
\(B. 13\)
\(C. 14\)
\(D. 15\)
\(E. 16\)


In a right triangle \(a^2+b^2=c^2\) and in an obtuse angle c becomes even bigger so \(a^2+b^2<c^2............9^2+12^2<c^2..........c^2>255\)
So C can be 16....
But say the largest side is 12, then \(9^2+c^2<12^2.....c^2<144-81......c^2<63.......c<8\)

Therefore either c>15 or c<8, hence ONLY 16 fits in...
E
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Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh  [#permalink]

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New post 13 Aug 2018, 05:26
=>


If a, b and c are sides of a right triangle and c is the longest side, then c^2 = a^2 + b^2.
If a, b and c are sides of an acute triangle and c is the longest side, then c^2 < a^2 + b^2.
If a, b and c are sides of an obtuse triangle and c is the longest side, then c^2 > a^2 + b^2.

Since 15^2 = 9^2 + 12^2 and 16 > 15, 16 could be the third side of the obtuse triangle.

Therefore, the answer is E.

Answer : E
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Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh &nbs [#permalink] 13 Aug 2018, 05:26
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