Optimizing Area with Perimeter Constraints

[physicsman2]

Homework Statement

the sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions of the triangle and the square that produce a minimum total area.

Homework Equations

The Attempt at a Solution

my problem is finding the primary and secondary equations.
is A=1/2bh+s^2 the primary equation and P=3b+4s the secondary equation

 

[Dick]

Seems ok so far. Now you want to express h in terms of b as well, right? b and h aren't independent.

 

[physicsman2]

how could i put h in terms of b
first i put b in terms of s and got (10-4s)/3 then put that into the area equation

 

[Dick]

You can put h in terms of b because it's an equilateral triangle. The height is directly proportional to the base. Use trig or pythagoras.

 

[physicsman2]

thank you very much