Answer:
The smallest possible whole-number length of the unknown side is [tex]19\ inches[/tex]
Step-by-step explanation:
we know that
The triangle inequality theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side
Let
x-----> the length of longest side
Applying the triangle inequality theorem
case A)
[tex]10+15 > x[/tex]
[tex]25 > x[/tex]
Rewrite
[tex]x< 25[/tex]
case B)
[tex]10+x > 15[/tex]
[tex]x > 15-10[/tex]
[tex]x> 5[/tex]
The solution of the third side is the interval-------> [tex](5,25)[/tex]
but remember that
In an obtuse triangle
[tex]x^{2} > a^{2} +b^{2}[/tex]
[tex]x^{2} > 15^{2} +10^{2}[/tex]
[tex]x > 18.03\ inches[/tex]
Round to a whole number
[tex]x= 19\ inches[/tex]
