Activity 3.4.4

[mikeshulman]

The solution to Activity 3.4.4 is written using values of a function "A", which is evidently the function that computes the area of the rectangle as a function of the x-coordinate of its right-hand side. But while that way of parametrizing the rectangles is a natural choice, it wasn't mentioned in the problem statement and other choices are possible, so I would suggest the solution be more explicit.

(The solution to Activity 3.4.5 also involves a not-previously-defined function "A", although in this case since the problem asks for an angle and shows an angle theta in the diagram, one is likely to guess that the input of A is the angle theta.)

Also I must say I'm not thrilled about maximizing the "combined perimeter and area", as perimeter and area have different units, so adding them together is not a physically meaningful operation.

[mattboelkins]

But while that way of parametrizing the rectangles is a natural choice, it wasn't mentioned in the problem statement and other choices are possible, so I would suggest the solution be more explicit.

I don't think that the solutions manual needs to explain all possible choices, or even several. The solution also states that a choice is being made:

"Letting x represent half the width of the rectangle's base, it follows that the rectangle's height is 25-x^2."

[mikeshulman]

The solution I'm looking at, in the back of the book, does not say anything about a choice being made or what $A$ or $x$ represents. It just says "Maximum area: $A(\frac{5}{\sqrt{3}}) = \frac{500}{9}\sqrt{3} \approx 96.225$".