Question

question
the lengths of the three sides of a triangle (in meters) are consecutive odd integers. if the
perimeter is 93 meters, find the value of the middle of the three side lengths.
answer
meters
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Explanation:

Step1: Let the middle side length

Let the middle side length be \(x\) meters. Then the other two side lengths are \((x - 2)\) meters and \((x+2)\) meters.

Step2: Use the perimeter formula

The perimeter of a triangle \(P=a + b + c\). Here, \(P=(x - 2)+x+(x + 2)\). Simplify the expression: \((x - 2)+x+(x + 2)=x-2+x+x + 2=3x\).

Step3: Solve for \(x\)

Since the perimeter \(P = 93\) meters, and \(P = 3x\), we have the equation \(3x=93\). Divide both sides by 3: \(x=\frac{93}{3}=31\).

Answer:

\(31\)