Question 880956
The area of a rectangle is 
{{{A=L*W=100}}}
The diagonal of a rectangle is,
{{{D^2=L^2+W^2}}}
From the area,
{{{L=100/W}}}
{{{L^2=10000/W^2}}}
Substituting
{{{D^2=10000/W^2+W^2}}}
Differentiating with respect to W,
{{{2D*(dD/dW)=-20000/W^3+2W}}}
Set the derivative equal to zero to get the minimum distance.
{{{dD/dW=(-20000/W^3+2W)/2D=0}}}
{{{20000/W^3=2W}}}
{{{W^4=10000}}}
{{{W=10}}}
Then,
{{{L=100/W}}}
{{{L=10}}}
The shortest diagonal occurs when the rectangle is actually a square.