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**furor celtica** the cross-section of an object has the shape of a quarter-circle of radius r adjoining a rectangle of width x and height r as shown in the diagram.

(A). the perimeter and area of the cross-section are P and A respectively. express each of P and A in terms of r and x, and hence show that A=0.5Pr - r^2

(B). taking the perimeter of the cross-section as fixed, find x in terms of r for the case when the area A of the cross section is a maximum, and show that for this value of x A is a maximum and not a minimum.

ok the part A. was no problem, but part B ? i kinda dont even understand what they are saying, perimeter 'as fixed'? i dont get. i don't understand how to logically combine the given equations, can someone help me work it through?