Consider the cross section of a house:
...|
../|\
./a| \c
/__|__\
|...b.|
|_____|

a. Solve this problem by the method of Lagrange multipliers. Use the Pythagorean theorem,
a2 + b2 = c2 (*)
to eliminate one of the variables, thus reducing the problem to three variables with one constraint and one multiplier.

‘a’ is to be the vertical height of the roof, ‘c’ the ‘length’ of the roof (from ridge to gutter) and ‘b’ the semi-width of the roof base.

pretty much minimize the perimeter subject to the area being 30 m2

Question

Consider the cross section of a house: 
...| 
../|\ 
./a| \c 
/__|__\ 
|...b.| 
|_____|

a. Solve this problem by the method of Lagrange multipliers. Use the Pythagorean theorem, 
a2 + b2 = c2 (*) 
to eliminate one of the variables, thus reducing the problem to three variables with one constraint and one multiplier.

‘a’ is to be the vertical height of the roof, ‘c’ the ‘length’ of the roof (from ridge to gutter) and ‘b’ the semi-width of the roof base.

pretty much minimize the perimeter subject to the area being 30 m2