Question

If the area of the largest square is 64 $c{m}^2$, the side length (in cm) of the smallest square will be:

• A. 2
• B. $2\sqrt{2}$
• C. $4\sqrt{2}$
• D. 4

Answer 1

The correct option is D 4

Given, area of the largest square, i.e. of S1 = 64 $c{m}^2$
Side of square S1 = $\sqrt{area}$ = $\sqrt{64}$ = 8 cm

Side of the square S1 = Diameter of the circle C1 = Diagonal of the square S2 = 8 cm
In the square S2,
$diagona{l}^2$ = $sid{e}^2$ + $sid{e}^2$
$\Rightarrow 8^2$ = $2sid{e}^2$
$\Rightarrow sid{e}^2=32$
$\Rightarrow side=\sqrt{32}=4\sqrt{2}$
$\therefore SideofthesquareS2=4\sqrt{2}$ cm

Side of the square S2 = Diameter of the circle C2 = Diagonal of the square S3 = $4\sqrt{2}$ cm
In the square S3,
$diagona{l}^2$ = $sid{e}^2$ + $sid{e}^2$
$\Rightarrow (4\sqrt{2}{)}^2$ = $2sid{e}^2$
$\Rightarrow sid{e}^2=16$
$\Rightarrow side=\sqrt{16}=4$
$\therefore SideofthesquareS3=4$ cm