Respuesta :

calculista

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of the triangle is greater than the length of the third side

so

[tex]AB+AC > BC\\AB+BC > AC\\AC+BC > AB[/tex]

we have

[tex]AB=12\ units\\AC=15\ units\\ BC=x\ units[/tex]

substitute the values

[tex]12+15 > x[/tex] ----->[tex]x < 27\ units[/tex]

[tex]12+x > 15[/tex] -----> [tex]x > 3\ units[/tex]

[tex]15+x > 12[/tex] -----> [tex]x > -3\ units[/tex]

[tex]3\ units < x < 27\ units[/tex]

therefore

the answer is

The value of x must be greater than [tex]3[/tex]

Answer:

x must be greater than 3

Step-by-step explanation:

If ABC is a triangle with sides a,b and c.

Then, it must satisfy:

a<b+c , b<a+c and c<a+b

Let a=12,b=15 and c=x

Then,  12<15+x , 15<12+x and x<12+15

i.e. -3<x , 3<x and x<27

Hence, x must be greater than 3 and less than 27 so that all the conditions are satisfied.

Hence, x must be greater than 3

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