Answer:
[tex]x=23/\sqrt{6}[/tex],
[tex]y= \frac{23}{6\sqrt{6}}[/tex]
Step-by-step explanation:
From the question we are told that
Surface area is 529 square meters
Generally the dimensions of the cuboid
[tex]v=x^y[/tex]
[tex]D=4xy+2x^2 =529[/tex]
[tex]V=x^29(\frac{529-6x^2}{4x})[/tex]
[tex]V' =529-6x^2/4[/tex]
[tex]v'=0[/tex]
Therefore
[tex]529=6x^2[/tex]
[tex]x=\sqrt{\frac{529}{6} }[/tex]
[tex]x=23/\sqrt{6}[/tex]
Mathematically
[tex]v''=\frac{12x}{4}[/tex]
[tex]v''=-3\frac{23}{\sqrt{6} }<0[/tex]
[tex]y= \frac{529-2*(\frac{529}{6} }{4*\frac{23}{\sqrt{6} } }[/tex]
[tex]y= \frac{23}{6\sqrt{6}}[/tex]
Therefore
[tex]x=23/\sqrt{6}[/tex]
and
[tex]y= \frac{23}{6\sqrt{6}}[/tex]
