Squaring a Rectangle
- Ku, Yin Bon (Albert)
Here is a very interesting construction problem: Suppose you are given a rectangle. How can your construct a square whose area equals the area of the given rectangle using straightedge and compass? This problem is called "squaring a rectangle". We can rephrase the problem as follows: Let a, b be the width and height of the given rectangle. Then the required square must have the side . Therefore, the problem boils down to "how can we construct a line segment of length if we are given the line segments of length a and b?" Take a look at the following diagram to get an idea on how to solve it ...
Question: You can drag the blue points to change the values of a and b. Can you express c in term of a and b? Hint: Use similar triangles.