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 length of a rectangular field is double its width. Inside the field,there is a square-shaped pond $8 \, m$ long. If the area of the pond is $\frac{1}{8}$ of the area of the field,what is the length of the field? (in $m$)

$A$ ladder is placed so as to reach a window $63 \ cm$ high. The ladder is then turned over to the opposite side of the street and is found to reach a point $56 \ cm$ high. If the ladder is $65 \ cm$ long,then the width of the street is........$cm$

The area of a triangle is $216 \, cm^{2}$ and its sides are in the ratio $3:4:5$. The perimeter of the triangle is ....... $cm$.

$A$ wire is in the form of a semi-circle of $7 \, cm$ radius. The length of the wire will be (in $cm$):

The area of a square is $1024\, cm^2$. What is the ratio of the length to the breadth of a rectangle whose length is twice the side of the square and breadth is $12\, cm$ less than the side of this square?