# Question :

Given a symmetrical Greek cross, the task is to cut the symmetrical Greek cross into five pieces, so that one piece shall be a smaller symmetrical Greek cross and the remaining four pieces will fit together and form a perfect square.

# Solution :

• If the smaller Greek cross is cut in the way shown below, then we will be dividing the cross into five parts of which four parts will be similar and the remaining part will be a Greek cross.
• Let the remaining four parts be A, B, C, and D then, these four parts can be used to form a square.
• The four remaining parts are similar to each other.
• The three sides of all these parts are equal.
• When two parts are joined as shown in figure 2 they form a rectangle. Here the length of the rectangle is twice the width of the rectangle.
• These four parts A, B, C, and D form two rectangles as shown below. Here A and C form a rectangle and B and D form another rectangle.
• Since, the length and width of both these rectangles are the same therefore square can be formed by joining these two rectangles as shown below:

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