Let's call the length of the rectangular prism "l", the width "w", and the height "h". We know that the surface area of the rectangular prism is 335 ft^2, so we can write an equation:
2lw + 2lh + 2wh = 335
We also know that the area of the base is 21 ft^2, so lw = 21. Finally, we know that the perimeter of the base is 20 ft, so 2l + 2w = 20, or l + w = 10.
We can use these equations to solve for h. First, we can solve for l or w in terms of the other variable:
l = 21/w
w = 21/l
Next, we can substitute these expressions into the equation l + w = 10:
21/w + 21/l = 10
Multiplying both sides by wl, we get:
21l + 21w = 10wl
Substituting 21/w for l and 21/l for w, we get:
21(21/w) + 21(21/l) = 10(21)
Simplifying this equation, we get:
441/w + 441/l = 210
Multiplying both sides by wl, we get:
441l + 441w = 210lw
Substituting 21/w for l and 21/l for w, we get:
441(21/w) + 441(21/l) = 210(21)
Simplifying this equation, we get:
9261/w = 441
Solving for w, we get:
w = 9261/441
w ≈ 21
Substituting this value of w into the equation l + w = 10, we get:
l + 21 = 10
l = -11
This doesn't make sense, so we made a mistake somewhere. Let's go back and check our work.
We made an error in the equation 441l + 441w = 210lw. We should have multiplied both sides by 2 instead of by wl. So, let's start again:
441/w + 441/l = 210/21
Multiplying both sides by wl, we get:
441l + 441w = 210
Substituting 21/w for l and 21/l for w, we get:
441(21/w) + 441(21/l) =