Start with a square of variable side with one vertex on the origin and one on the positive x-axis:
The problem is to create a rectangle with the same area as the square whose sides are in the ratio 2:1.
Creating the initial square in GeoGebra
- Add a point A at the origin.
- Add a point B on the x-axis.
- Use the Regular Polygon tool selecting vertices at A and B and set the number of vertices to 4.
Creating the initial square in TI-Nspire
- Add a new Graphs page.
- Add a point at the origin by finding the Intersection Point of both axes .
- Add a new Point On the x-axis.
- Display the Coordinates of this point.
- Use Measurement Transfer to transfer the value of the x-coordinate to the y-axis.
- Add a line Perpendicular to the axis through the point on x-axis.
- Add a line Perpendicular to the axis through the point on y-axis.
- Find the Intersection Point of the two lines.
- Add a Polygon through the four points. NB it is important to use the Polygon tool and not the Rectangle tool.
- Measure the Area of the square.