The perimeter of a triangle is 30 in. The longest side is 2 less than 3 times the shortest side and the other side is 2 more than twice the shortest side. Find the length of each side

Shortest side=5, Largest side=13, Other side=12

Step-by-step explanation:

Let's define the shortest side of the triangle as x, since the other two sides are defined in terms of this one.

The longest side is 2 less than 3 times the shortest side, then it is 3 * x - 2.

The other side is 2 more than twice the shortest side, then it is 2 * x + 2.

By the problem directions, we know that the perimeter or sum of sides is 30.

x + 3x - 2 + 2*x + 2 = 30

Adding all the terms "with x" together and all terms "without x" together, we get ...

6*x = 30

Solving for x (dividing both sides by 6), we get ...

x = 30/6 = 5

Finally,

Shortest side: 5

Largest side: 3 * 5 - 2 = 13

Other side: 2 * 5 + 2 = 12