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Answer :

Given the shown triangle with the lengths of two sides:

[tex](5n+6),(4n+5)[/tex]

Given the perimeter of the triangle : ( 17n + 11)

The perimeter of the triangle is the sum of the sides lengths

Let the third side length = L

So,

[tex]L+(5n+6)+(4n+5)=17n+11[/tex]

Solve to find L:

[tex]\begin{gathered} L+5n+6+4n+5=17n+11 \\ L+9n+11=17n+11 \\ L=17n-9n+11-11 \\ L=8n \end{gathered}[/tex]

So, the length of the third side = 8n

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