Question

The value of x must be greater than .

Answer 1

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

Answer 2

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

$AB+AC > BC\\AB+BC > AC\\AC+BC > AB$

we have

$AB=12\ units\\AC=15\ units\\ BC=x\ units$

substitute the values

$12+15 > x$ ----->$x < 27\ units$

$12+x > 15$ -----> $x > 3\ units$

$15+x > 12$ -----> $x > -3\ units$

$3\ units < x < 27\ units$

therefore

the answer is

The value of x must be greater than $3$