One side of triangle is 6 more than 2 times the shortest side. The third side is 14 feet more than the shortest side. The perimeter is 84. Find all three sides

In ascending order, the side lengths are {16, 30, 38}.

Step-by-step explanation:

Represent the shortest side by s.

Building on this, we represent the next side as 2s + 6.

The third and last side is then s + 14.

The perimeter is the sum of the lengths of these 3 sides and has the value 84. Thus, s + 2s + 6 + s + 14 = 84.

Combining the s terms, we get:

4s + 6 + 14 = 84, or

4s + 20 = 84, or

4s = 64. Therefore, s = 64/4 = 16

The length of the shortest side is 16; that of the next side is 2 (16) + 6, or 38, and that of the third side is 16 + 14, or 30.

Check: Do 16, 38 and 30 sum up to 84, as they must?

Do 16 and 68 sum up to 84?

Is 84 = 84? YES. Answers are correct.