Question

A rectangular package can be sent through the mail only if the sum of its length and girth is not more than 120". find the dimensions of the box of maximum volume that can be sent if the base of the box is square.

Answer 1

Knowing that a square gives the optimum area; 

120=s²
√120=s 
√2×2×2×5×3=s
2√2×3×5=s
2√30=s 

Therefore, the length should be ≈10.95" 

Hope I helped :) 

Answer 2

The answer I got is: 40x20x20 where the length is 40 and the height and width are 20 each.  Here's my work: (Let me know if you have any questions.