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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If the interior angles of a triangle are in the ratio 3 to tagged by: Max@Math Revolution ##### This topic has 6 expert replies and 1 member reply ### GMAT/MBA Expert ## If the interior angles of a triangle are in the ratio 3 to ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 B. 45 C. 60 D. 75 E. 90 _________________ Math Revolution 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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Max@Math Revolution wrote:
[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
B. 45
C. 60
D. 75
E. 90
All 3 angles must add to 180°
So, if we divide 180° into 3 angles in the ratio 3 : 4 : 5, we get: 45° : 60° : 75°

What is the measure of the largest angle?
The largest angle is 75 degrees°

Cheers,
Brent

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Last edited by Brent@GMATPrepNow on Wed Sep 12, 2018 9:09 am; edited 1 time in total

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Brent@GMATPrepNow wrote:
Max@Math Revolution wrote:
[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
B. 45
C. 60
D. 75
E. 90
We should recognize that 3, 4, 5 are the lengths on a Pythagorean triplets (RIGHT triangles with INTEGER lengths)
This means a triangle with lengths 3, 4, 5 (or any triangle with side lengths in those same ratios) must be a RIGHT TRIANGLE

What is the measure of the largest angle?
The largest angle in a RIGHT triangle is 90 degrees (and the other two angles must add to 90 degrees)

Cheers,
Brent
He's comparing angles not lengths

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regor60 wrote:
He's comparing angles not lengths
Oops, good catch!
I have edited my response accordingly.

Cheers and thanks,
Brent

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Max@Math Revolution wrote:
[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
B. 45
C. 60
D. 75
E. 90
The sum of the 3 angles of a triangle = 180.
The sum of the parts of the ratio = 3+4+5 = 12.
Since 180/12 = 15, the multiplier for the ratio is 15, implying that the largest angle = 5*15 = 75.

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Max@Math Revolution wrote:
[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
B. 45
C. 60
D. 75
E. 90
$\left( {{\text{ALL}}\,\,{\text{in}}\,\,{\text{degrees}}} \right)$
Trivial application of the k technique, simple and powerful tool of our method:
$? = 5k\,\,\,\,\,\,\left( {k > 0} \right)$
$3k + 4k + 5k = 180$
$12k = 180\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,\,\,\frac{5}{{12}}} \,\,\,\,\,? = 5k = \frac{5}{{12}}\left( {180} \right) = 75$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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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, x + y + z = 3k + 4k + 5k = 12k = 180, and so k = 180 /12 = 15.
Therefore, the largest angle of the triangle is z = 5k = 5(15) = 75.

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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 Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2012 messages Followed by: 15 members Upvotes: 43 Max@Math Revolution wrote: [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 B. 45 C. 60 D. 75 E. 90 We can re-express the ratio of the three angles as 3x : 4x : 5x, and, since the sum of the interior angles of a triangle is 180 degrees, we have: 3x + 4x + 5x = 180 12x = 180 x = 15 Thus, the largest angle is 5(15) = 75 degrees. Answer: D _________________ Scott Woodbury-Stewart Founder and CEO • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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