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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7597
GMAT 1: 760 Q51 V42
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The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh  [#permalink]

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09 Aug 2018, 01:33
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Difficulty:

35% (medium)

Question Stats:

63% (01:29) correct 37% (01:40) wrong based on 52 sessions

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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 18 Jun 2018 Posts: 267 Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh [#permalink] ### Show Tags 09 Aug 2018, 02:05 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 $$225< 256$$ Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4512 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh [#permalink] ### Show Tags 09 Aug 2018, 09:19 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) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Retired Moderator Joined: 30 Jan 2015 Posts: 805 Location: India Concentration: Operations, Marketing GPA: 3.5 Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh [#permalink] ### Show Tags 09 Aug 2018, 09:24 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. _________________ The few, the fearless ! Thanks Math Expert Joined: 02 Aug 2009 Posts: 7764 Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh [#permalink] ### Show Tags 09 Aug 2018, 09:27 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 _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7597 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh [#permalink] ### Show Tags 13 Aug 2018, 06:26 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: The lengths of two sides of a certain obtuse triangle are 9 and 12. Wh   [#permalink] 13 Aug 2018, 06:26
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