Ratio of sides

Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.

Correct result:

S =  157.6174 cm2

Solution:

r=9 cm r2=(a/2)2+(b/2)2 a:b=2:7  r2=(a/2)2+((7/2 a)/2)2 r2=a2/4+a2 (7/4)2  a=r/(1/4+(7/4)2)=9/(1/4+(7/4)2)4.945 cm  b=7/2 a=7/2 4.94517.3074 cm  o=2 (a+b)=2 (4.945+17.3074)44.5048 cm  o=2π r1  r1=o/(2π)=44.5048/(2 3.1416)7.0832 cm   S=π r12=3.1416 7.08322=157.6174 cm2



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