If the length of a rectangle is increased in the ratio $6:7$ and its breadth is diminished in the ratio $5:4$,then its area will be changed in the ratio:

The difference of the areas of two squares drawn on two line segments of different lengths is $32 \, cm^2$. Find the length of the greater line segment if one is longer than the other by $2 \, cm$. (in $cm$)

An error of $2 \%$ in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is.....$\%$

The sum of the circumference of a circle and the perimeter of a square is equal to $272 \, cm$. The diameter of the circle is $56 \, cm$. What is the sum of the areas of the circle and the square? (in $cm^2$)

If the perimeter of a rectangular field is $200\, m$ and its breadth is $40\, m$,then its area is (in $m^2$):

What is the perimeter of an equilateral triangle whose area is $4 \sqrt{3} \text{ cm}^2$?