Question

Find the radius of a circle whose area equals the area of a rectangle that measures 2 ft by 1 ft

Answer 1

Area of rectangle = 2 × 1 = 2 ft²

Area of rectangle = area of circle = 2 ft²

πr² = 2

22/7 × r² = 2

r² = 7/11

r = 0.7977 ft

Answer 2

the area of a rectangle is well, just length * width, so 2x1, or just 2 then

now, what's the radius of a circle with an area of 2?


`\bf \textit{area of a circle}\\\\ A=\pi r^2\qquad \begin{cases} r=radius\\ ------\\ A=2 \end{cases}\implies 2=\pi r^2\implies \cfrac{2}{\pi }=r^2 \\\\\\ \boxed{\sqrt{\cfrac{2}{\pi }}=r}`