# Cannot express limits in arrays

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James Rodriguez on 5 Mar 2020
Commented: Sindar on 5 Mar 2020
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.

Sindar on 5 Mar 2020
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)

#### 1 Comment

Sindar on 5 Mar 2020
If you have a condition that is not already satisfied (here, Y<=100), you can enforce it manually:
A = 4345;
Z = [33:0.000001:sqrt(A)];
Y = A./Z;
Z(Y>100) = [];
Y(Y>100) = [];

Walter Roberson on 5 Mar 2020
Edited: Walter Roberson on 5 Mar 2020
A = 4345;
Z = 33:0.000001:sqrt(A);
Y = A ./ Z;
Reconstructed_A = Z .* Y;
IYY = 1/2 * Z .* Y.^3;
subplot(1,2,1)
plot(Y, A-Reconstructed_A);
subplot(1,2,2)
plot(Y, IYY)