Problem 1_7



Given three squares arranged in a rectangle of dimensions u × v, find the area of the smallest square in terms of u and v.


First, I created the outside rectangle. Next, I created 2 points one on side u and the other on the side adjacent to u (not v). Next, I created a regular polygon (square) using the segment I created with those two points. This made the biggest square inside of the rectangle. Next, I created another point on side u and used the upper right vertex of the previous square to make a line segment. I created another regular polygon using this segment (This is my smallest square). Next, I used the lower right vertex of the biggest square and a point on the side of the bigger rectangle (adjacent to v) to create a line segment. I then created another regular polygon. I played with the three squares until it looked like the construction given.