Question

The value of x must be greater than
.

Answer 1

x must be greater than 3

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`