If $D, E$ and $F$ are the mid-points of the sides of an equilateral triangle $ABC,$ then the ratio of the area of triangle $DEF$ and $DCF$ is

$A$ man runs round a circular field of radius $50\, m$ at the speed of $12\, km/hr$. What is the time taken by the man to take twenty rounds of the field? (in $minutes$)

The area of a rhombus is $150 \, cm^2$. The length of one of its diagonals is $10 \, cm$. The length of the other diagonal is ....... $cm$.

The perimeter of an isosceles right-angled triangle is $2p \, cm$. Its area is

The smallest side of a right-angled triangle is $8\, cm$ less than the side of a square of perimeter $56\, cm$. The second largest side of the right-angled triangle is $4\, cm$ less than the length of the rectangle of area $96\, cm^2$ and breadth $8\, cm$. What is the largest side of the right-angled triangle? (in $cm$)

If the area of an equilateral triangle is equal to the area of an isosceles triangle whose base and equal sides are $16 \, cm$ and $10 \, cm$ respectively,then the side of the equilateral triangle is......$cm$