Sum of two smaller sides of a triangle must be greater than the largest side. So, the required range value is 7 < x < 23.
Triangle:
Important information:
- The measure of two sides of a triangle are 8 and 15.
- The measure of third side is x.
Sum of two smaller sides of a triangle must be greater than the largest side.
If x is the largest side of the triangle, then
[tex]8+15>x[/tex]
[tex]23>x[/tex] ...(i)
If 15 is the largest side of the triangle, then
[tex]x+8>15[/tex]
[tex]x>15-8[/tex]
[tex]x>7[/tex] ...(ii)
Using (i) and (ii), we get
[tex]7<x<23[/tex]
Therefore, the required range value is [tex]7<x<23[/tex].
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