Example 2 - Algebraic solution
GeoGebra
Area can be expressed as a quadratic function of the base (x) under the condition: x + 2h = 10, where h is the height of the rectangle. By calculating the coordinates of the vertex we get the result. It can be proved by writing the quadratic equation into GeoGebra's Input Bar to get the graph. If our equation is correct, the points from section 3 will lie on it. By using the command Extreme the coordinates of vertex will appear in the algebraically window [or following similar procedure with TI-Nspire™]
Here the screencast with the approach shown in GeoGebra is presented.
Solution with TI-Nspire™
      
Other approaches