polynomial functions...is what i did right?

Question

Jimmie is building a sandbox that is 12 times as wide as it is deep, and 1m longer than it is wide. It holds 3m^3 of sand when full. The wood cost $24/m^2. How much will the wood cost Jimmie? (btw, there is no top or bottom, just the sides when calculating for the area!!) (that the question...now i got the answer $84....is that right??? if so, can someone confirm that? if not , how would you get the correct answer....) ?? thanks!!

Answer 1

12x *x *(12x +1) = 3

144x^3 + 12x^2 - 3 = 0

solve for x

24$* (2*x*12x +2*x*(12x+1)) = $$$

plug in x

Answer 2

Depth = d
Width = 12d
Length = 12d + 1

Volume = depth * width * length
= d * 12d * (12d + 1)
= 3

so 12d^2(12d + 1) = 3
144d^3 + 12d^2 = 3
144d^3 + 12d^2 - 3 = 0

(4d-1)(36d^2+12d+3) = 0
d = 1/4
so width = 12/4 = 3
and heigth = 3 + 1 = 4


Surface area of box (excluding top / bottom) is
2 * (w*h) + 2 (d*h) or
2 * (3*4) + 2(1/4 * 4) = 24 + 2 or 26

If wood costs $24 / meter square and we need 26 square meters, then we have to spend 24*26 dollars or $624

Answer 3

h = depth
width = 12h
length = 12h+1
So h(12h)(12h+1) = volume = 3 m^3
144h^3 +12h^2 = 48h^3 + 4h^2 -1 = 0
h approximately = .268 m
so width = 12(.268) = 3.216 m
length = 4.216 m
Area = 2hl +2hwl
2(.268*4.216 + .268*3.216 = 14.864 m^2
So cost = 14.864*24 = $356.74