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# If the interior angles of a triangle are in the ratio 3 to 4 to 5, wha

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7372
GMAT 1: 760 Q51 V42
GPA: 3.82
If the interior angles of a triangle are in the ratio 3 to 4 to 5, wha  [#permalink]

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12 Sep 2018, 02:45
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Difficulty:

25% (medium)

Question Stats:

72% (00:35) correct 28% (00:21) wrong based on 24 sessions

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[Math Revolution GMAT math practice question]

If the interior angles of a triangle are in the ratio $$3$$ to $$4$$ to $$5$$, what is the measure of the largest angle?

A. $$30^0$$
B. $$45^0$$
C. $$60^0$$
D. $$75^0$$
E. $$90^0$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 18 Jul 2018 Posts: 908 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: If the interior angles of a triangle are in the ratio 3 to 4 to 5, wha [#permalink] ### Show Tags 12 Sep 2018, 02:49 The sum of the interior angles in a triangle is 180. Sum of the ratios of the triangle is 3x+4X+5x = 180. x = 15. Largest angle is 5x = 5*15 = 75. D is the answer. _________________ Press +1 Kudo If my post helps! Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7372 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If the interior angles of a triangle are in the ratio 3 to 4 to 5, wha [#permalink] ### Show Tags 14 Sep 2018, 00:40 => Let $$x, y$$ and $$z$$ be interior angles of the triangle. Since $$x:y:z = 3:4:5$$, we can write $$x = 3k, y = 4k$$ and $$z = 5k$$. Since the interior angles of the triangle add to $$180^o, x + y + z = 3k + 4k + 5k = 12k = 180^o,$$ and so $$k = \frac{180^o}{12} = 15^o.$$ Therefore, the largest angle of the triangle is $$z = 5k = 5(15) = 75^o.$$ Therefore, the answer is D. Answer: D _________________ 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$149 for 3 month Online Course"
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Re: If the interior angles of a triangle are in the ratio 3 to 4 to 5, wha   [#permalink] 14 Sep 2018, 00:40
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