The perimeter of a rectangular deck is 216 feet. the area is 2,691 square feet. what are the dimensions of the deck?

Perimeter (p) of a rectangle = 2w+2l, or p/2 = w+l, 216 = 2w+2l, 108 = w+l
area (a) of a rectangle = l×w
So a = 2691 = l×w, l = 2691/w
p = 216 = 2w+2l, so 216 = 2w+2(2691/w)
216 = 2w + 5382/w
216 = 2w^2/w + 5382/w
216 = (2w^2 + 5382)/w
216w = 2w^2 + 5382
2w^2 -216w + 5382 = 0
2 (w^2 -108w + 2691) = 0
w^2 -108w + 2691 = 0
For this you really have to "plug and play" unless you have a graphing calculator. For instance, you need the sum of width (w) and length (l) to be 108. Also the product of w×l needs to be 2691. And I can only assume due to complexity that your teacher wants while numbers of feet for w and l.
So with your calculator start with a number less that 50, and divide 2691 by that. Why?? Because 50×50 = 2500 (close to 2691), and we want two different numbers because a rectangle has different widths than lengths.
So I jumped to 45, not a whole # answer, then 44, nope. 43, nope. 42, no. 41, no. 40, no. 39... yes!! 2691÷39 gives you 69, a whole #!
Now the real test: does 39+69 = 108... yes! We've got our length and width (but kinda cheated lol)! ;)
39ft × 69ft