A rectangle has 225 square cm of area. What dimensions result in the least perimeter?
(calculus)

Question

A rectangle has 225 square cm of area. What dimensions result in the least perimeter? 
(calculus)

shane_b · Answer

For the calculus method you can do this: http://www.algebra.com/algebra/homework/word/geometry/Geometry_Word_Problems.faq.question.317038.html In reality, I'd just do this:$$L_{side}=\sqrt{225}=15cm$$$$P=4L=4(15cm)=60cm$$

fellowroot · Answer

Find least perimeter.

What do we want? P=2L +2W
What do we have? A=LW
                          A=225
                          225=LW
Plug what we have into what we want.
                         W=225/L
                         P=2L+2(225)/L
                         P=2L+450/L
To max or min, take derivative, then set derivative equal to zero.
                        dP/dL =2 -450/L^2
                        0=2-450/L^2
                        0=2L^2-450
For L                 Squrt(225) = L
                        15 =L
Now remember....
                        A=LW=225, L=15
                            15W=225
                               W=15
                       L and W are a min when L=W=15

....this problem was solved by Eric S. badass math and physics major who will get his phd!