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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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