Precalculus math problem

Question

The lengths of the sides of a triangle are consecutive even integers. The perimeter of the triangle is equal to the perimeter of a square whose side measures 5 less than the shortest side of the triangle. Find the length of the longest side of the triangle.

Answer 1

So, if the sides are a difference of 2, then they can be expressed as x, x+2 and x+4. Adding these gives 3x+6. The problem says this perimeter is equal to perimeter of a square whose side = x-5. So 3x+6=4(x-5). Combining like terms yields x=26. So the length of the longest side of the triangle is x+4=26+4=30.