Cut out a square of side 8 centimeter. Cut this suitlably and join with a suitable square to make a large square of area 80 square centimeter.
The square is of the side = 8cm
Area of the first square = 8×8=64 sq.units
It is cut and rearranged to get a bigger square with a square hole in the middle. [1]
The side of the square hole in the middle = x cm
The area of the square hole in the middle = x×x=x2 sq.units
∴ The area of the bigger square = area of the 1st square + area of the square hole in the middle [2]
∴ The area of the bigger square = 64 sq.units + x2 sq.units = 80 sq.units
x2 = 16
x = 4 cm
So, the side of the suitable smaller square is 4 centimeter. [2]