Question 746229: please help me solve this equation ; the circle is divided into 4 parts a,b,c,d where part a & c form a semicircle and part b&d form the other semicircle area of part a to area of part c is in the ratio 1: 3 the area of part b to the area of part d is in the ratio 1:2. the area of part c is bigger than part b by 20 SquareCentimeters find the area of the whole cirle
Answer by savvyhush23(50)   (Show Source):
You can put this solution on YOUR website! please help me solve this equation ; the circle is divided into 4 parts a,b,c,d where part a & c form a semicircle and part b&d form the other semicircle area of part a to area of part c is in the ratio 1: 3 the area of part b to the area of part d is in the ratio 1:2. the area of part c is bigger than part b by 20 SquareCentimeters find the area of the whole cirle.
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Ok, let solve it one by one,
Let,
At = Total area of circle
Aa = Area of a
Ab = Area of b
Ac = Area of c
Ad = Area of d
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part a & c form a semicircle...part b&d form the other semicircle:
 , and 
part a to area of part c is in the ratio 1:3... , or 
part b to the area of part d is in the ratio 1:2... , or 
the area of part c is bigger than part b by 20...
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Ok, here is my favorite part:
We have 5 unknown (At, Aa, Ab, Ac, and Ad), so we have to form 5 equations to solve it. The 4 equations are ready above,
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since a & c and b & d are semi circle,  , equation 5
we have the 2 equations for that above, substituting here,  , or  , then add this to the other 3 remaining equation: 
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but  and  , so,  ,
So,  ,  ,  , and 
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Therefore, 
Check it, the value of individual area must satisfy the given ratio.
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