anonymous 4 years ago 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

|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