$1.$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 $76$ feet, what are the lengths of the three sides?

The shortest side of the deck is feet.

$($Simplify your answer.$)$

$2.$ A recycling bin is in the shape of a rectangular box. Find the height of the box if its length is $15ft,$ its width is $8ft,$ and its surface area is $562f{t}^2.($In the figure, $h=$ height. Assume that the given surface area includes that of the top lid of the box.$)$

The height of the box is

$ft.$