Three shapes

1/5 of a circle is shaded. The area's ratio of a square and the sum of a| rectangle and the circle is 1:2. 60% of the square is shaded, and 1/3 of the rectangle is shaded. What is the ratio of the area of the circle to that of the rectangle?

Correct answer:

C =  0.3333

Step-by-step explanation:


R = 1
R/3+C/5 = 0.60·S
2·S = C+R

R = 1
3C+5R-9S = 0
C+R-2S = 0

Pivot: Row 1 ↔ Row 2
3C+5R-9S = 0
R = 1
C+R-2S = 0

Row 3 - 1/3 · Row 1 → Row 3
3C+5R-9S = 0
R = 1
-0.667R+S = 0

Row 3 - -0.66666666666667 · Row 2 → Row 3
3C+5R-9S = 0
R = 1
S = 0.667


S = 0.66666667/1 = 0.66666667
R = 1/1 = 1
C = 0-5R+9S/3 = 0-5 · 1+9 · 0.66666667/3 = 0.33333333

C = 1/3 ≈ 0.333333
R = 1
S = 2/3 ≈ 0.666667

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