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?

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