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What is the ratio of the green area to the blue area?

 

 May 6, 2020
 #1
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0

Split green square in half; we have 2 identical rectangles. Rectangle's diagonal is the radius of the semi circle.

 

Ratio of rectangle's short side to long side is  1 : 2

 

The angle between the radius and the longer rectange side is     tan(A) = 1 / 2 = 26.56505118°

 

Let the radius  r = 1

 

Green square side    a = cos(A) = 0.894427191

 

Green  area          Ag = a² = 0.8 u²

 

Blue square diagonal is the radius and it is also  r = 1

 

Blue square side      b = sqrt(1/2) = 0.707106781

 

Blue  area              Ab = 2 * b² = 1 u²   

 

The ratio of the  green  area to the  blue  area is  4 : 5  indecision

 May 6, 2020
edited by Dragan  May 6, 2020
edited by Dragan  May 6, 2020
 #2
avatar+109519 
+1

Hint:

Let the radius equal a set value. You can choose any number or numeral.    

Now work out the dimensions of the sides

etc

 

I'll help more but I want evidence that you are listening.

Show us what you can do by yourself.

 

 

Dragon may have seen an easier way ... 

 May 6, 2020

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