Question

geometry the expression $17n + 11$ represents the perimeter of the triangle. what is the length
the length of the third side is
explain your reasoning.

Explanation:

Step1: Recall perimeter formula

The perimeter \( P \) of a triangle is the sum of its three sides. Let the three sides be \( a \), \( b \), and \( c \). So \( P = a + b + c \). We know \( P = 17n + 11 \), \( a = 5n + 6 \), and \( b = 4n + 5 \). We need to find \( c \).

Step2: Rearrange formula to solve for \( c \)

From \( P = a + b + c \), we can rearrange to \( c = P - a - b \).

Step3: Substitute the known expressions

Substitute \( P = 17n + 11 \), \( a = 5n + 6 \), and \( b = 4n + 5 \) into the formula for \( c \):

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Answer:

The length of the third side is \( 8n \).