Question

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.

Answer 1

The square is of the side = 8cm

Area of the first square = $8\times 8=64sq.units$

It is cut and rearranged to get a bigger square with a square hole in the middle.$\left[1\right]$

The side of the square hole in the middle = x cm

The area of the square hole in the middle = $x\times x=x^{2}sq.units$

$\therefore$ The area of the bigger square = area of the 1st square + area of the square hole in the middle$\left[2\right]$

$\therefore$ The area of the bigger square = 64 sq.units + $x^{2}sq.units$ = 80 sq.units
$x^2$ = 16
x = 4 cm
So, the side of the suitable smaller square is 4 centimeter.$\left[2\right]$