The lengths of the sides of a triangle are consecutive even integers. Find the length of the longest side if it is 22 units shorter than the perimeter.:

Since the sides are consecutive even integers:

x = one side

x + 2 = 2nd side

x + 4 = 3rd side

x + 4 = x + x + 2 + x + 4 - 22 {the longest side is 22 shorter than perimeter}

x + 4 = 3x - 16 {combined like terms}

2x = 20 {added 16 and subtracted x from both sides}

x = 10 {divided both sides by 2}

x + 2 = 12 {substituted 10, in for x, into x + 2}

x + 4 = 14 {substituted 10, in for x, into x + 4}

**14 is the longest side**

*© Algebra House*