The sides of a triangle are in the ratio $\frac{1}{4}: \frac{1}{6}: \frac{1}{8}$ and its perimeter is $91\, cm$. The difference of the length of the longest side and that of the shortest side is

$ABCD$ is a cyclic quadrilateral. $AB$ and $DC$ when produced meet at $P$. If $PA = 8 \ cm$,$PB = 6 \ cm$,and $PC = 4 \ cm$,then the length (in $cm$) of $PD$ 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

The radius of a circular wheel is $1 \frac{3}{4} \text{ m}$. How many revolutions will it make in travelling $11 \text{ km}$?

In a parallelogram,the lengths of adjacent sides are $12\, cm$ and $14\, cm$,respectively. If the length of one diagonal is $16\, cm$,then find the length of the other diagonal (in $cm$).

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