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
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