The cost of carpeting a room $5 \ m$ wide with carpet at ₹ $3.50$ per $m^2$ is ₹ $105$. The length of the room is ...... $m$.

$A$ circle and a rectangle have the same perimeter. The sides of the rectangle are $18 \, cm$ and $26 \, cm$. What is the area of the circle? (in $cm^2$)

The length of a rectangle is twice the diameter of a circle. The circumference of the circle is equal to the area of a square of side $22\, cm$. What is the breadth of the rectangle if its perimeter is $668\, cm$? (in $cm$)

In a quadrilateral $ABCD$,the sides $AB, BC, CD, DA$ measure $20\, m, 13\, m, 17\, m$ and $10\, m$ respectively,and the diagonal $AC$ is $21\, m$. The area of the quadrilateral is ........ $m^2$.

The ratio of the area of a sector of a circle to the area of the circle is $1:4$. If the area of the circle is $154 \, cm^2$,the perimeter of the sector is ........ $cm$.

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?