Ruler and Compass Construction
Square with Same Area as Given Rectangle

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1. Extend ray AB
2. Circle centered at B, radius BC
3. Circle centered at A, arbitrary radius
4. Circle centered at E, same radius
5. Segment FG, so H is midpoint of AE
6. Circle centered at H, through A
7. Extend ray BC
8. IB is the side of the square
9. Circle centered at B, radius IB
10. Circle centered at J, radius IB
11. Circle centered at I, radius IB
12. Square HJKI
13. Right triangles show IB/AB = BE/IB