Perimeter and integers?

Question

The length 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. How do I find the length of the longest side of the triangle. I'm studying for a test and cannot figure out this answer. Any help would be appreciated!

Answer 1

Ok.

Call the 3 sides of the triangle x, x+2 and x+4.

Meaning the perimeter of the triangle is 3x + 6.

Call the side of the square x - 5, because it's 5 less than the shortest length of the triangle.

Meaning the perimeter of the square is 4x - 20.

The perimeters are equal to eachother, therefore

4x - 20 = 3x +6

x = 26

The longest length of the triangle is x + 4.

Therefore the longest length = 30.

Answer 2

To answer this question, you are given the lengths of the triangle. They would be, x, x+2, x+4, for consecutive even integers. Then it tells you that the perimeter of the triangle equals to (x-5)+(x-5)+(x-5)+(x-5), (the parenthesis are for clarity, not order of operations). so this means x+x+2+x+4 which is 3x+6, is equal to (x-5)+(x-5)+(x-5)+(x-5), which is 4x-20. Solving 3x+6 = 4x-20 gives x = 26. This means the longest side of the triangle is 30.