What is the Area of the largest equilateral triangle that can inscribed in a 2 x 2 square?
How can geogebra answer the question for us?
1)Place point A at (0,0)
2)Place point B at (0,2)
3)Draw a slider with MIn = 0, Max = 2 and Inc = .001. Call it b.
4)Place point C at (2,2).
5)Draw a line segment BC. Color it red. Draw point (2,0) and label it D. Draw line segment CD and color it red. This represents our square.
6)Place a point at (b,2).
This is done by entering P = (b,2).
7)Use the regular polygon tool and select P then A and in the input box enter 3 and equilateral triangle APE is created.
8)Draw a line through E and perpendicular to the x axis.
9)Get the insection of this line and the x axis by using the intersect 2 objects tool. It will be labelled F.
10)You can hide E and now highlight the slider point called b and use the arrow keys and and shift arrow keys until F is as close to (2,0) as is possible. I set the rounding option to 15 digits for this.
11)After doing that I was able to get F = (2.000000807568878, 0). Now just read off poly1 = 1.856407210140189. That is the largest area based on the accuracy of our drawing.
Read off d = 2.070552778849165 as the sides of that triangle.
12)Put a point G on the bottom of the triangle and measure GAF. I get
Check to see how this compares to the math solution at http://www.mathisfunforum.com/viewtopic … 92#p204492
where the answer given is 15° for the angle and
for the sides. Pretty good accuracy from geogebra!
Here is the drawing