In a triangle $ABC$,$AB + BC = 12 \text{ cm}$,$BC + CA = 14 \text{ cm}$,and $CA + AB = 18 \text{ cm}$. Find the radius of the circle (in $\text{cm}$) which has the same perimeter as the triangle.

The length of a rectangular plot is $20 \ m$ more than its breadth. If the cost of fencing the plot at $₹ 26.50/m$ is $₹ 5300$,what is the length of the plot in metres?

In the given figure,$ABCD$ is a square. $EFGH$ is a square formed by joining the midpoints of the sides of $ABCD$. $LMNO$ is a square formed by joining the midpoints of the sides of $EFGH$. $A$ circle is inscribed inside $LMNO$. If the area of the circle is $38.5 \text{ cm}^2$,then what is the area (in $\text{cm}^2$) of square $ABCD$?

The length of a rectangle is $3/5$ of the side of a square. The radius of a circle is equal to the side of the square. The circumference of the circle is $132 \, cm$. What is the area of the rectangle if the breadth of the rectangle is $8 \, cm$? (in $cm^2$)

$A$ circular road runs around a circular garden. If the difference between the circumference of the outer circle and the inner circle is $44\, m$,then find the width of the road in $m$.

If the sides of a rectangle are increased by $20 \%$,the percentage increase in its perimeter is