Answer :
Answer:
The shortest side of the deck is 17 feet.
The second side of the deck is 23 feet.
The third side of the deck is 28 feet.
Step-by-step explanation:
Let x represent the length of shortest side of the triangular deck.
We have been given that the second side of a triangular deck is 6 feet longer than the shortest side, so the length of second side would be [tex]x+6[/tex].
We are also told that the third side is 6 feet shorter than twice the length of the shortest side, so the length of third side would be [tex]2x-6[/tex].
Since the perimeter of the deck is 68 feet, so sum of lengths of all sides of deck would be equal to 68.
[tex]x+x+6+2x-6=68[/tex]
Let us solve for x.
[tex]x+x+2x+6-6=68[/tex]
Combine like terms:
[tex]4x=68[/tex]
Divide both sides by 4:
[tex]\frac{4x}{4}=\frac{68}{4}[/tex]
[tex]x=17[/tex]
Therefore, the shortest side of the deck is 17 feet.
The length of second side would be: [tex]x+6\Rightarrow 17+6=23[/tex]
Therefore, the second side of the deck is 23 feet.
the length of third side would be: [tex]2x-6\Rightarrow 2\cdot 17-6=34-6=28[/tex]
Therefore, the third side of the deck is 28 feet.