MATLAB: Cannot express limits in arrays

Question

I cannot think of the correct title for this problem I am having so I apolgise for that initially.

I have a rectangle with fixed area , 4345. The height(Y) and width(Z) however change. Y is equal to or greater then Z. Z has a minimum value 33 and Y has a maximum value 212. I belive the minimum of Y and maximum of Z must be sqrt(4345) . I am trying to create a code that will let me multiply Z and Y together, while understanding their product will always be A.

A = 4345;
Z = [33:0.000001:sqrt(A)];
Y = [sqrt(A):0.000001:212];
A = Z*Y;
IYY = 1/12*Z*Y^3

However the problem is the arrays are not consistent. I thought about not using the arrays, in hope MatLab would understand that ZY would always equal A, however it then wont recognise Z or Y. without the array I dont know how to implement my limits of each. My end goal is to be able to plot how IYY changes for diffrent values of Y.

Answer 1

If the area is fixed, you don't want independent Y and Z:

A = 4345;
Z = [33:0.000001:sqrt(A)];
Y = A./Z;

Note that the condition Y<212 is guaranteed by Z>33 (4345/33 ~ 131)