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 $m$)

Seven equal cubes each of side $5 \, cm$ are joined end to end. Find the surface area of the resulting cuboid? (in $cm^2$)

Three equal cubes are placed adjacently in a row. Find the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes.

The area of a sector of a circle of radius $5 \, cm$,formed by an arc of length $3.5 \, cm$,is (in $cm^2$)

The area of a square is $196 \, cm^2$. Its side is half the radius of a circle. The circumference of the circle is equal to the breadth of a rectangle. If the perimeter of the rectangle is $712 \, cm$,what is the length of the rectangle? (in $cm$)

Find the area of an isosceles right-angled triangle whose hypotenuse is $8\, cm$.