A zoo wishes to construct an aquarium in the shape of a rectangular prism such that the length is twice the width and 5m greater than the height. If the aquarium must have a volume strictly between 1125m^3 and 3000m^3, determine the restrictions on the length of the aquarium.

Answer 1

let the length be x
let the width be x/2
let the height be x-5

x(x/2)(x-5) > 1125
x^2(x-5) ≥ 2250
let's solve x^2(x-5) = 2250
with the help of Wolfram

http://www.wolframalpha.com/input/?i=solve+x%5E2(x-5)+%3D+2250

x = 15

x(x/2)(x-5) < 3000
x^2(x-5) = 6000 and that gives me x = 20

so 15 < x < 20