GMAT Math Assistance » Problem-Solving Questions » Geometry » Triangles » Acute / Obtusage Triangles » Calculating the size of the side of an acute / obtuse triangle

Two sides of a triangle meacertain 5 inches and also 11 inches. Which of the complying with statements properly expresses the range of feasible lengths of the third side

*
?


*
 is the biggest of the 3 sidelengths. 

Then 

*
. How many feasible worths does 
*
have? 


*


*


*


*


None of these statements have the right to be proved without even more information.

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The triangle is scalene and also ideal.


The triangle is scalene and acute.



Correct answer:

The triangle is scalene and obtusage.


Explanation:

If these are the measures of the interior angles of a triangle, then they total 

*
. Add the expressions, and also settle for 
*
.

*

*

*

*

One angle measures 

*
 The others measure:

*

*

Due to the fact that the largest angle steps better than 

*
, the angle is obtuse, and also the triangle is too. Because the 3 angles each have actually various meacertain, their oppowebsite sides execute likewise, making the triangle scalene.



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*


*



Correct answer:


Explanation:

The 3 sides of a scalene triangle have various steps, so 15 deserve to be removed.

By the Triangle Inetop quality, the sum of the lengths of the 2 smaller sides have to exceed the size of the third side. Since 

*
, 8 violates this theorem; since 
*
, 22 does also. 

10 is a valid measure of the 3rd side, since 

*



Explanation:

By trial and also error, we acquire four methods to include distinctive primes to yield sum 33:

*
 

*

*

*

In each situation, however the Triangle Inetop quality is violated - the amount of the two shortest lengths does not exceed the third. 

No triangle deserve to exist as defined.



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*


*



Explanation:

A scalene triangle has actually three sides of different lengths, so we are searching for three unique prime integers whose sum is a prime integer. 

One of the sides cannot be 2, given that the amount of 2 and two odd primes would be an even number greater than 2, a compowebsite number. As such, start via the leastern 3 odd primes, add enhancing triples of unique prime numbers, as complies with, until a solution presents itself:

*
 - incorrect

*
 - correct

The correct answer, 19, presents itself quickly.



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This triangle cannot exist.


*



Explanation:

A scalene triangle has actually three sides of different lengths, so we are searching for 3 distinctive prime integers whose sum is 47. 

There are ten methods to include 3 distinctive primes to yield amount 47:

*

*

*

*

*

*

*

*

*

*

By the Triangle Inetop quality, the sum of the lengths of the shortest two sides have to exceed that of the biggest. We have the right to therefore remove all yet four:

*

*

*

*

The best possible length of the longest side is 23.



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*


*



Explanation:

The three sides of a scalene triangle have different measures. One measure 

*
 cannot have is 12, however this is not an option.

It cannot be true that 

*
. Because the perimeter is 

*
, we have the right to find out what various other worth deserve to be removed as follows:

*

*

*

As such, if , then 

*
, and the triangle is not scalene. 9 is the correct alternative.



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This triangle cannot exist.


*



Explanation:

We are searching for methods to include 3 primes to yield a sum of 43. Two or all 3 (considering that an equilateral triangle is thought about isosceles) need to be equal (although, given that 43 is not a multiple of 3, just two have the right to be equal).

See more: The Error Involved In Making A Certain Measurement, (Get Answer)

We will collection the shared sidelength of the congruent sides to each prime number in turn approximately 19:

*

*

*

*

*

*

*

By the Triangle Inequality, the sum of the lengths of the shortest 2 sides should exceed that of the greatest. We deserve to therefore get rid of the initially three. 

*
*
, and 
*
 include numbers that are not prime (21, 15, 9). This leaves us through just one possibility:

*
 - best length 19

19 is the correct choice.



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