Find the dimensions of a rectangle with area 216 m2 whose perimeter is as small as possible. (if both values are the same number, enter it into both blanks.)

1. Let the width of the rectangle be a, and its height be b.

a*b=216, so b=216/a

2. the perimeter of the rectangle is P=2a+2b=2a+2(216/a)=2a+432/a

since a varies, and P also varies accordingly, we can write P as a function in variable a as follows:



3. Taking the derivative we find the critical points where we have the largest or smallest values the function may take:









or

4. Since  would be negative with the negative root, the largest value of P is when a=14.7

5. b=216/a=216/14.7=14.7

[14.7, 14.7]   (or [square root 216, square root 216])