Question

Can you draw a square whose area is double the area of the square below?

Answer 1

We know that the area of a square is double the area of another square if the length of the side of the former is equal to the length of the diagonal of the latter.

Let the length of each side of a given square be x units.

Length of diagonal of this square = units = units

So, the length of each side of the required square is units.

The following steps should be followed to draw the required square.

(1) Draw two squares of side x units, adjacent to each other.

(2) Cut the two squares along their diagonals.

(3) Place the triangles in such a way that the obtained quadrilateral is also a square.

The square so obtained has each side equal to the diagonal of the given square.

Thus, the obtained square has an area double the area of the given square.