Length of a rectangular field is 200\% of the radius of a circular field, which has a circumference of $264 ext{ meters}$. If the area of the rectangular field is $2016 ext{ meters}^2$, then find by what percentage the radius of the circular field is more than the breadth of the rectangular field.

Question

Length of a rectangular field is 200\% of the radius of a circular field, which has a circumference of $264 	ext{ meters}$. If the area of the rectangular field is $2016 	ext{ meters}^2$, then find by what percentage the radius of the circular field is more than the breadth of the rectangular field.

Accepted Answer

**Solution:**

1. Given the circumference of the circular field is $264 	ext{ m}$. Using the formula for circumference:
   $$2 \pi r = 264$$
   $$r = \frac{264}{2 \pi} = \frac{264}{2 	imes 3.14} = \frac{264}{6.28} = 42 	ext{ meters}$$

2. Length of the rectangular field is $200\%$ of the radius:
   $$	ext{Length} = 2 	imes r = 2 	imes 42 = 84 	ext{ meters}$$

3. Area of the rectangular field is given as $2016 	ext{ m}^2$:
   $$	ext{Area} = 	ext{Length} 	imes 	ext{Breadth}$$
   $$2016 = 84 	imes 	ext{Breadth}$$
   $$	ext{Breadth} = \frac{2016}{84} = 24 	ext{ meters}$$

4. Now, find by what percentage the radius is more than the breadth:
   $$	ext{Percentage increase} = \frac{r - 	ext{Breadth}}{	ext{Breadth}} 	imes 100 = \frac{42 - 24}{24} 	imes 100 = \frac{18}{24} 	imes 100 = 75\%$$

**Answer:** 75\%

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