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Math 126
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Question 9

Step 1
Extend the base line of the rectangle to the left. The extension should be longer than the height of the rectangle.

 

 

 

step1.gif (885 bytes)
Step 2
Draw a circular arc with center at the blinking lower left corner of the rectangle, and the radius of the arc is exactly the height of the rectangle.

 

 

 

step2.gif (1382 bytes)
Step 3
Find the midpoint of AB by constructing a perpendicular bisector of AB.
The procedure is exactly the same as those in question 1, so we only show you the diagram here.
step3.gif (18730 bytes)
Step 4
Connect a line through the intersection of the two green arc and hence mark the midpoint of AB.
step4.gif (3449 bytes)
Step 5
Let C be the midpoint, then draw a circular arc centered at C and with radius AC (or equivalently BC).

 

 

 

step5.gif (9856 bytes)
Step 6
Extend the left vertical edge of the rectangle upwards until it intersects the orange arc. Mark the intersection (as indicated by the red dot)

 

 

 

 

Step 7
The height of the red dot will then be the height of the required square.
You can use your favorite method to construct the green square (which will have the same area as the rectangle.)

 

 

 

 

          

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