The radius of Circle A is three feet less than twice the diameter of Circle B. If the sum of the diameters of both circles is 49 feet, find the area and circumference of Circle A.

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Rebekah Irvine · Accepted Answer

Step 1Let the radius and diameter of circle A be&amp;nbsp;rA&amp;nbsp;and&amp;nbsp;dA&amp;nbsp;respectively.Let the radius and diameter of circle B be&amp;nbsp;rB&amp;nbsp;and&amp;nbsp;dB&amp;nbsp;respectively.The diameter of circle B is three feet less than the radius of circle A, which indicatesrA=2dB−3&amp;nbsp;(1)49 feet is the combined diameter of both circles, which translates todA+dB=49&amp;nbsp;(2)From the equation (2) we get,dB=49−dASubstituting&amp;nbsp;dB=49−dA&amp;nbsp;in equation (1)rA=2(49−dB)−3rA=98−2dA−3rA=95−2dA&amp;nbsp;(3)Step 2We know that&amp;nbsp;Radius=Diameter2So,&amp;nbsp;dA=2rAThen the equation&amp;nbsp;rA=95−2×2rArA=95−4rArA+4rA=95rA=955rA=19Therefore the radius of the circle A is 19 feetStep 3Circumference of circle&amp;nbsp;A=2πrACircumference of circle&amp;nbsp;A=2×3.14×19&amp;nbsp;feetCircumference of circle&amp;nbsp;A=119.32&amp;nbsp;feetArea of circle of&amp;nbsp;A=πrA2Area of circle&amp;nbsp;A=3.14×192&amp;nbsp;feetArea of circle&amp;nbsp;A=1133.54&amp;nbsp;feet2

The radius of Circle A is three feet less than

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