Question
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 ?
Answer: Option E
$$\eqalign{
& 2\pi R = 2\left( {l + b} \right) \cr
& \Rightarrow 2\pi R = 2(26 + 18)cm \cr
& \Rightarrow R = \left( {\frac{{88}}{{2 \times 22}} \times 7} \right)cm \cr
& \Rightarrow R = 14\,cm \cr} $$
∴ Area of the circle :
$$\eqalign{
& = \pi {R^2} \cr
& = \left( {\frac{{22}}{7} \times 14 \times 14} \right)c{m^2} \cr
& = 616\,c{m^2} \cr} $$
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$$\eqalign{
& 2\pi R = 2\left( {l + b} \right) \cr
& \Rightarrow 2\pi R = 2(26 + 18)cm \cr
& \Rightarrow R = \left( {\frac{{88}}{{2 \times 22}} \times 7} \right)cm \cr
& \Rightarrow R = 14\,cm \cr} $$
∴ Area of the circle :
$$\eqalign{
& = \pi {R^2} \cr
& = \left( {\frac{{22}}{7} \times 14 \times 14} \right)c{m^2} \cr
& = 616\,c{m^2} \cr} $$
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