If the diagonals of a rhombus are $8$ and $6,$ then the square of its side is

The area of a rectangle is thrice that of a square. The length of the rectangle is $20\,cm$ and the breadth of the rectangle is $\frac{3}{2}$ times that of the side of the square. The side of the square (in $cm$) is

$A$ wire bent in the form of a circle of radius $42 \, cm$ is bent in the form of a rectangle whose sides are in the ratio of $6:5$. The smaller side of the rectangle is (in $cm$)

The ratio of bases of two triangles is $x: y$ and that of their areas is $a: b$. Then the ratio of their corresponding altitudes will be

$A$ vessel is in the form of a hollow cylinder mounted on a hemispherical bowl. The diameter of the hemisphere is $14 \, cm$ and the total height of the vessel is $13 \, cm$. Find the capacity of the vessel in $cm^3$. (Take $\pi = 22/7$)

Each side of a rhombus is $26 \ cm$ and one of its diagonals is $48 \ cm$ long. The area of the rhombus is (in $cm^2$)