GMAT Math assist » Problem-Solving concerns » Geometry » triangle » Acute / Obtuse triangle » Calculating the length of the next of one acute / obtuse triangle

Two sides of a triangle measure 5 inches and 11 inches. I m sorry of the following statements properly expresses the range of feasible lengths of the 3rd side

*
?


*
 is the best of the three sidelengths. 

Then 

*
. Just how many possible values does 
*
have? 


*


*


*


*


None of this statements can be proved without additional information.

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The triangle is scalene and also right.


The triangle is scalene and also acute.



Correct answer:

The triangle is scalene and obtuse.


Explanation:

If these are the procedures of the inner angles the a triangle, then they total 

*
. Include the expressions, and solve for 
*
.

*

*

*

*

One edge measures 

*
 The rather measure:

*

*

Since the biggest angle measures higher than 

*
, the edge is obtuse, and also the triangle is as well. Since the three angles each have various measure, their opposite sides perform also, making the triangle scalene.



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*


*



Correct answer:


Explanation:

The three sides of a scalene triangle have different measures, so 15 can be eliminated.

By the Triangle Inequality, the sum of the lengths the the two smaller sides should exceed the length of the 3rd side. Since 

*
, 8 violates this theorem; since 
*
, 22 does as well. 

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

*



Explanation:

By trial and also error, we obtain four ways to add distinct primes to yield sum 33:

*
 

*

*

*

In every case, yet the Triangle Inequality is violated - the sum of the two shortest lengths does not exceed the third. 

No triangle can exist together described.



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*


*



Explanation:

A scalene triangle has actually three sides of various lengths, so we are trying to find three distinctive prime integers whose amount is a element integer. 

One that the sides cannot be 2, since the amount of 2 and two odd primes would certainly be an even number greater than 2, a composite number. Therefore, beginning with the the very least three weird primes, add increasing triples of distinct prime numbers, as follows, until a equipment presents itself:

*
 - incorrect

*
 - correct

The correct answer, 19, presents itself quickly.



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This triangle can not exist.


*



Explanation:

A scalene triangle has three sides of various lengths, so us are searching for three distinctive prime integers whose amount is 47. 

There are ten ways to add three distinct primes to yield sum 47:

*

*

*

*

*

*

*

*

*

*

By the Triangle Inequality, the amount of the lengths that the shortest two sides should exceed the of the greatest. We can thus eliminate all however four:

*

*

*

*

The greatest feasible length that the longest next is 23.



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*


*



Explanation:

The 3 sides that a scalene triangle have different measures. One measure 

*
 cannot have actually is 12, yet this is no a choice.

It can not be true that 

*
. Because the perimeter is 

*
, we can discover out what other value deserve to be got rid of as follows:

*

*

*

Therefore, if , then 

*
, and the triangle is not scalene. 9 is the exactly choice.



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This triangle can not exist.


*



Explanation:

We are searching for ways to add three primes to productivity a sum of 43. Two or all 3 (since an it is provided triangle is thought about isosceles) have to be equal (although, because 43 is no a multiple of three, only two deserve to be equal).

See more: 83 Cm Is How Many Inches - Convert 83 Centimeters To Inches

We will set the mutual sidelength the the congruent sides to each prime number consequently up to 19:

*

*

*

*

*

*

*

By the Triangle Inequality, the sum of the lengths that the shortest 2 sides need to exceed that of the greatest. We can as such eliminate the very first three. 

*
*
, and 
*
 include number that space not element (21, 15, 9). This leaves united state with just one possibility:

*
 - best length 19

19 is the correct choice.



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