We can let
...[1]
Therefore, the perimeter can be expressed as
...[2]
Continue by expressing P in terms of T alone. Then, differentiate, set to 0 and solve for T. You can also express it in terms of w instead of T.
Consider a window the shape of which is a rectangle of height h surmounted a triangle having a height T that is 1.5 times the width w of the rectangle (as shown in the figure below).
If the cross-sectional area is A, determine the dimensions of the window which minimize the perimeter.
h=?
w=?