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The sides of a triangle are 7, 12, and x.  What are all possible values of x?

 Feb 19, 2021
 #1
avatar+31009 
0

Triangle side length rule

 

7 + x     must be greater than 12          x >5

 Feb 19, 2021
 #2
avatar+944 
+2

We can use the triangle inequality. The sum of two sides must be greater than the third:

 

7 + 12 > x

7 + x > 12

12 + x > 7

 

Solving, we get:

19 > x

x > 5

x > -5

 

We get the inequality 5 < x < 19, so there are 12 possible values of x: 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18.

 Feb 19, 2021
 #3
avatar+31009 
0

Good work , CTP....I forgot to calculate the MAXIMUM   ....but you didn't !    ~ EP

 Feb 19, 2021

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