The length of a plot is double its width. If a square piece of land of area $150 \, m^2$ occupies $\frac{1}{3}$ area of the plot,then what is the length of the plot? (in $m$)

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 ....... $cm$.

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

Each side of an equilateral triangle is increased by $1.5 \%$. The percentage increase in its area is......$\%$

The two adjacent sides of a parallelogram are $60 \, m$ and $40 \, m$ and one of the diagonals is $80 \, m$ long. The area of the parallelogram is

$A$ 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 $m^2$)?