Decorating the tree

A symmetric tree has decorative lines of equal slope, and of lengths 11 and 13. What is the area ratio of green to red to brown?

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Green : red : brown is 1331 : 528 : 338.

Solution by Stéphane Bernard.

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One reply on “Decorating the tree”

G=green area
R=red area
B= brown area

G+R is similar to triangle G
So G+R = (13/11)^2 G
Also easy is (G+R+B)/(G+R)= 13/11.
So G:G+R:G+R+B. = 11^3: 11*13^2: 13^3

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