Question

question
the lengths of the three sides of a triangle (in centimeters) are consecutive integers. if the perimeter is 24 centimeters, find the value of the middle of the three side lengths.
answer
centimeters
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Explanation:

Step1: Set up the equation

Let the three consecutive integers be \(n - 1\), \(n\), \(n+ 1\). The perimeter of a triangle is the sum of its sides. So, \((n - 1)+n+(n + 1)=24\).

Step2: Simplify the equation

Combine like - terms: \((n - 1)+n+(n + 1)=n-1 + n+n + 1=3n\). So, \(3n = 24\).

Step3: Solve for \(n\)

Divide both sides of the equation \(3n = 24\) by \(3\). We get \(n=\frac{24}{3}=8\).

Answer:

\(8\)