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Math Revolution GMAT Instructor V
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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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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Director  D
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]

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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.
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Math Revolution GMAT Instructor V
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]

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=>

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

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