Optimization. A rectangle is to have an area of 32 square cms. Find its dimensions so that
the distance from one corner to the mid point of a non-adjacent edge is a
minimum

Question

Optimization.  A rectangle is to have an area of 32 square cms. Find its dimensions so that
the distance from one corner to the mid point of a non-adjacent edge is a
minimum

anonymous · Answer

|dw:1328207321371:dw| xy = 32 makes y = 32/x

$$z^2 = (32/x)^2 + (x/2)^2$$
Isolate z
$$z = 32/x + x/2$$
Find dz/dx
$$f \prime(z) = (x^2-64)/(2x^2)$$

Set z' = 0, algebraically solving for x having 
$$x = \pm8$$
Since you cannot have a dimension of -8, the only answer for x is 8.

Go back to the original area equation; 32 = xy and plug in x making 
32 = 8y 
y = 4