Max/minimisation new question (1 Viewer)

[enigma_1]

A wire of length L is available for making a circle and a square. How should the wire be divided between the 2 shapes to maximise the sum of the enclosed area?

Please help ,thanks

 

[QZP]

Let length used for square be x, and length used for circle be L-x

Now,
Area of square A1= (x/4)^2
Area of circle A2 = (L-x)^2 / 4pi ---- Play around with 2pi.r (circumference of circle)= L-x

Therefore total A = A1 + A2 ---- Which is a quadratic in x (or L if you like)

Try to get to the maximum for A now I'll help you more if you need it

Edit: I think it may be easier to switch around the lengths i.e. use L-x for square, and x for circle. Sorry I should have saw that coming