The lengths of the three sides of a triangle (in inches) are consecutive odd integers. If the perimeter is 6363 inches, find the value of the middle of the three side lengths.

In Geometry, a triangle is a three-sided polygon that consists of three edges and three vertices. The most important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

Perimeter :

The perimeter of a triangle is defined as the total length of its boundary. A triangle is a polygon with 3 sides and it can be classified into different types based on the measure of its sides and angles

Now, according to the question:

If the middle of the three consecutive odd integers is n, then the smallest is n +1 , the largest is n+2 and we have:

The perimeter of the triangle is as follows;

Therefore, Perimeter = n + (n + 1) + (n + 2)

⇒ 6363 = 3n + 3

⇒ 6363 - 3 = 3n

⇒ 6360 = 3n

⇒ n = 2120 inches

Therefore, the value of middle of the three side of length is 2120 inches.

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