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

The perimeter of a right triangle is $12 \, cm$. The hypotenuse is $5 \, cm$. What are the other two sides and the area of the triangle?

$A$ rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn,which has an area of $240 \, m^2$. If the width of the path is $3 \, m$ and the length of the path is greater than its breadth by $2 \, m$,what is the area of the rectangular plot (in $m^2$)?

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 $cm$)

The area of an equilateral triangle is $9 \sqrt{3} \ m^{2}$. The length (in $m$) of the median is

$A$ triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is $100 \, m$,then the altitude of the triangle is