Answer: The required lengths of the three sides of the deck are 17 feet, 23 feet and 28 feet.
Step-by-step explanation: Given that the second side of a triangular deck is 6 feet longer than the shortest side and a third side that is 6 feet shorter than twice the length of the shortest side.
The perimeter of the deck is 68 feet.
We are to find the lengths of the three sides of the deck.
Let x feet be the length of the shortest side.
Then, according to the given information,
the length of the second side = (x+6) feet
and
the length of the third side = (2x-6) feet.
Since the perimeter of the deck is 68 feet, so we must have
[tex]x+x+6+2x-6=68\\\\\Rightarrow 4x=68x=\dfrac{68}{4}\\\\\Rightarrow x=17.[/tex]
Therefore the lengths of the three sides are
17 feet, (17+6) feet and (2×17-6) feet
= 17 feet, 23 feet and 28 feet.
Thus, the required lengths of the three sides of the deck are 17 feet, 23 feet and 28 feet.
