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## Which object weighs the same as the four squares?

### Solution

To start, we have
Using (1) and adding an ellipse to the four squares, we get
We have
Using (3), we get
Using (2) and (4), we get
Using (5) and eliminating an ellipse from each side, we get
Finally, Using (1) and (6) we get
The rectangle weighs the same as the four squares.

### Algebraic solution : Which object weighs the same as the four squares?

Let: S be the weight of one square, R the weight of one rectangle and E the weight of one ellipse.
R = 2 S + E           (1)
4E = 2R               (2)
Using (1), we get
4S = 2R – 2E               (3)
Using (2) and (3), we get
4S = 2R R = R
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