$A$ square has an area of $200\, m^2$. $A$ new square is formed such that the length of its diagonal is $\sqrt{2}$ times the diagonal of the given square. What is the area of the new square in $m^2$?

The sides of a triangle are $50 \, cm$,$78 \, cm$,and $112 \, cm$. The smallest altitude is $........... \, cm$.

$A$ circular park has a path of uniform width around it. The difference between the outer and inner circumferences of the circular path is $132 \, m$. Its width is.....$m$.

$A$ wire is in the form of a circle of radius $42 \ cm$. It is bent into a square. The side of the square is? (in $cm$)

The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side $22\, cm$. What is the breadth of the rectangle if its perimeter is $668\, cm$? (in $cm$)

The length of a rectangle is $3/5$ of the side of a square. The radius of a circle is equal to the side of the square. The circumference of the circle is $132 \, cm$. What is the area of the rectangle if the breadth of the rectangle is $8 \, cm$? (in $cm^2$)