Question

The area of a circular field is equal to the area of a rectangular field. The ratio of the length and the breadth of the rectangular field is $14:11$ respectively and perimeter is $100$ meters. What is the diameter of circular field?

• A. $14$m
• B. $22$m
• C. $24$m
• D. $28$m

Answer 1

The correct option is D $28$m

Let the length and breadth of rectangle be $14x$ & $11x$ metres respectively.
According to the question,
$2(14x+11x)=100$
$50x=100$
$x=2$
$\therefore l=14\times 2=28m$ & $b=11\times 2=22m$
We know that,
Area of rectangular field = $28\times 22m^2$
Given that
$\therefore Areaofcircularfield=Areaofrectangularfield$
$\pi r^2=28\times 22m^2$
$r^2=\frac{28\times 22}{22}\times 7\Rightarrow r=14m$
$d=2r=2\times 14=28m$.