The length of the third side of a triangle must be greater than the subtraction of the other two sides,
[tex]\begin{gathered} \text{The other two sides are 10 and 5 units} \\ \text{Difference of the other two sides= AC-AB =10-5=5 units} \end{gathered}[/tex]
And the length of the third side of a triangle must be less than the addition of the other two sides,
[tex]\text{Addition of the other two sides =10+5= 15 units}[/tex]
The length of the third should be less than 15 but greater than 5,
Hence, the most possible length of BC in triangle ABC is 15 units.
