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An acute triangles two sides measure 8 and 15. How many possible lengths are there for the third side if it is an integer?

 Feb 9, 2019
 #1
avatar+98090 
+1

Using the Triangle Inequality we have that

 

8 + 15 > x

 

23 > x

 

Also

 

8 + x > 15

 

x > 7

 

So.....the unknown side x  can be

 

7 < x < 23

 

And there are   15  integers between 7 and 23

 

 

cool  cool  cool

 Feb 9, 2019
 #2
avatar+23 
+1

The answer is wrong because it has to be an acute triangle. Most of the 15 integers make the triangle an obtuse angle.

robotjeremyc  Feb 10, 2019
 #3
avatar+98090 
+1

Thanks....I missed the "acute" part

 

The triangle  will be obtuse if  this is true

 

missing side > sqrt ( 15^2 + 8^2) 

 

missing side > sqrt (289)

 

missing side > 17

 

And when x = 17...we have a right triangle

 

So.... the triangle will be acute when  x =    8, 9, 10, 11, 12, 13, 14, 15, 16

 

So....9 values are possible for an acute triangle

 

 

cool cool cool

CPhill  Feb 10, 2019

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