I am trying to construct for my students the situation in Maple how to calculate the maximum area of a right triangular garden, if the perimeter is 60 meters long, and the two known sides are x, y and the third side is z and is part of the garden which isn't covert by the perimenter fence.
perimenter P = 60 -> x+y = 60
Next using the Pythagoran theorem and solve.
solve(x^2+z^2=y^2) and maple gives the solution z = sqrt(-x^2+y^2)
The area of the right triangle is T = 1/2*x*z
where y can be found solve(x+y=60,y) - > y = 60-x
I insert this into the formula for my area formula.
T(x) = 1/2*x*(sqrt(-x^2+(60-x)^2)
I solve(T'(x)=0) and get x = 20.
However if I wanna show the that they can insert x = 20 into T(x), then the following happens.
T(20) = 1/2*20*(sqrt(-x^2+(60-x)^2)
meaning Maple only inserts 20 the first x and not the second or third x. Any idea why this happens? Does Maple think that the second and third x are functions?