The three sides of a triangle are consecutive even integers. If the perimeter of the triangle is 72 inches, find the lengths of the sides of the triangle

n-2 , n , n+2

so
n-2 + n + n+2 = 72
3 n = 72
n = 24
22 24 26

To find the lengths of the sides of the triangle, we can set up an equation based on the given information.

Let's assume the three sides of the triangle are x, x+2, and x+4, where x is an even integer. Since the sides are consecutive even integers, we add 2 and 4 to the first side.

According to the definition of the perimeter, it is the sum of the lengths of all sides of the triangle. Therefore, we can write the equation as:

x + (x + 2) + (x + 4) = 72

Now, let's solve the equation to find the value of x:

3x + 6 = 72 (combine like terms)
3x = 72 - 6 (subtract 6 from both sides)
3x = 66 (simplify)
x = 66 / 3 (divide both sides by 3)
x = 22

So, the first side of the triangle is 22 inches. To find the lengths of the other two sides, we can substitute x into the expressions:

First side: x = 22 inches
Second side: 22 + 2 = 24 inches
Third side: 22 + 4 = 26 inches

Therefore, the lengths of the sides of the triangle are 22 inches, 24 inches, and 26 inches.

(1/3) * 72 = 24