ratio of areas inside the three squares
Geometry
Level
2
Three identical squares are arranged as shown. Their centers are connected to form an isosceles triangle. What is the ratio of the area of the green region to the area of the yellow region?
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1 solution
The area of the yellow portion of the triangle (calling the edge of each square 1) = (b h)/2= (1/2 1/2)/2=1/8. The green portion of the triangle = (a+b)h/2=((1/2+1)*1/2)/2=3/8.
Therefore the green area = 1-1/8+3/8=1.25 The yellow area=2-3/8+1/8=1.75
The ratio is 1.25:1.75 = 5:7