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If the interior angles of a triangle are in the ratio 3 to

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If the interior angles of a triangle are in the ratio 3 to

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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
B. 45
C. 60
D. 75
E. 90

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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°

Answer: D

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)

Answer: E

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.

The correct answer is D.

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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.

Therefore, the answer is D.
Answer: D

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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
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

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