Question

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 48 feet, what are the lengths of the three sides?

The shortest side of the deck is __ feet.
The second side of the deck is __ feet.
The third side of the deck is __ feet.

Answer 1

The shortest side of the deck is 12 feet. The second side is 15 feet. The third side is 21 feet.

Step-by-step explanation:

Let x be the length of the shortest side of the deck.

The second side is 3 feet longer than the shortest side, so its length is x + 3.

The third side is 3 feet shorter than twice the length of the shortest side, so its length is 2x - 3.

The perimeter of a triangle is the sum of the lengths of its sides. We can set up an equation to find x:

x + (x + 3) + (2x - 3) = 48

Combining like terms, we get 4x = 48, so x = 12.

The shortest side of the deck is 12 feet. The second side is 12 + 3 = 15 feet. The third side is 2(12) - 3 = 21 feet.