Consecutive Integer Problems – Linear

Question

The lengths of the three sides of a triangle (in feet) are consecutive even integers. If the perimeter is 6060 feet, find the value of the shortest of the three side lengths.

Answer 1

The problem states that the lengths of the sides of the triangle, in feet, are consecutive EVEN integers. If the shortest side is x feet long, then the next shortest side is (x+2) feet long and the longest side is (x+4) feet long.

The perimeter is calculated by summing the lengths of the three sides. Therefore,

x + (x + 2) + (x + 4) = 6,060

3x + 6 = 6,060

3x = 6,054

x = 2018

so 2018 feet is the length of the shortest side of the triangle.

Answer 2

Let x represent the shortest side. Then the other sides measure x+1 and x+2 feet, respectively, since the lengths of the sides are consecutive integers.

The perimeter is the sum of the lengths of the sides, so

x + ( x+1 ) + ( x + 2 ) = 6060

Combining like terms,

3x + 3 = 6060

Subtracting 3 from both sides,

3x = 6057

Dividing both sides by the coefficient of the variable:

x = 2019.

To check, we can add up these 3 numbers:

2019 + 2020 + 2021 which does. Indeed, sum up to 6060.