# Isoperimetric problem

### From Glossary

Among all closed plane curves with a given
perimeter find one that maximizes the area. This is also known as
*Queen Dido's problem* and serves as a classical problem
for variational calculus. Its significance in mathematical programming is that
it led to Lagrange's multiplier theorem. Restricting shapes to rectangles, the
problem is:

where is the perimeter. For positive and and multiplier , Lagrange's multiplier conditions requires and , so , which means the solution is the square.