1. The problem statement, all variables and given/known data This is from the book Calculus Single Variable, 4th edition: The cross-section of a tunnel is a rectangle of height h surmounted by a semicircular roof section of radius <i>r</i>. If the cross-sectional area is A, determine the dimensions of the cross section which minimize the perimeter. 2. Relevant equations I guess I am just lost on how to even approach this problem. I know you will need to use the formula for perimeter but do you need to even use the semicircle? Is the A refering to the rectangular section? To see a picture of this: http://www.wiley.com/college/sc/hugheshallett/chap4.pdf and it is question number 25 in section 4.5. (Problems) 3. The attempt at a solution I would start out by calling the height h and then the base of the rectangle d or diameter because the base is the same as the diameter of the circle on top. I would then note that the area of the rectangle is h times d and then i think i would need the formula for area or circumfrence of a circle so that i could fill "d" in with something. I guess i know what i would need to use, i think, i just don't know how to use it.