The second side of a triangular deck is 3 feet longer than the shortest side, and the third side is 3 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 80 feet, what are the lengths of the three sides?

Answer: the lengths are 20 feet, 23 feet and 37 feet

Step-by-step explanation:

Let x represent the length of the shorter side of the triangular deck.

The second side of a triangular deck is 3 feet longer than the shortest side. This means that the length of the second side is (x + 3) feet.

The third side is 3 feet shorter than twice the length of the shortest side. This means that the length of the third of the triangle is (2x - 3) feet.

If the perimeter of the deck is 80 feet, it means that

x + x + 3 + 2x - 3 = 80

4x = 80

x = 80/4

x = 20

The length of the second side is

20 + 3 = 23 feet

The length of the third side is

20 * 2 - 3 = 40 - 3 = 37 feet