Execute the following steps in Sketchpad concerning the way the area and perimeter of a tr...

Execute the following steps in Sketchpad concerning the way the area and perimeter of a triangle may vary.

[l] Construct segment and any line ℓ parallel to . (One way to do this is to construct line , translate it using Translate from the TRANSFORM menu, and finally, hide the line leaving just the segment.)

[2] Select a point C on line ℓ, and with C still selected, select A and B (with shift key depressed). Choose Polygon Interior from the CONSTRUCT menu. This will enable you to measure the area and perimeter of ΔABC.

[3] Select the interior of ΔABC and choose Area and Perimeter from the MEASURE menu. (At this point Area ΔABC and Perimeter ΔABC will be displayed on the screen for observation.)

By dragging point C along line ℓ, find what behavior concerning area and perimeter occurs. When is the area/perimeter maximum or minimum? If you can, explain the phenomena from basic geometric principles.

Area CAB = 1.1215 inches2

perimeter CAB = 5.244 inches