SOLUTION: Lines drawn parallel to the base of the triangle pictured, separate the other two sides into 10 equally spaced parts. What percentage of the triangle is grey?

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Question 1198962: Lines drawn parallel to the base of the triangle pictured, separate the other two sides into 10 equally spaced parts. What percentage of the triangle is grey?
Found 3 solutions by Alan3354, lotusjayden, ikleyn:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
pictured where?
Answer by lotusjayden(18)   (Show Source): You can put this solution on YOUR website!
The image is here
.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
The area of the k-th triangle is    of the area of the greatest triangle, A.


Therefore, the area of k-th individual single shape is  

     -   of the area of greatest triangle, A,    (1)

or

     =  = .    (2)



From here, the area of the grey part is

    A(grey) =  = .      (3)

(summing all (2k-1) over k = 1, 3, 5, 7, 9)



The area of the unshaded (white) part is

    A(white) =  = .    (4)

(summing all (2k-1) over k = 2, 4, 6, 8, 10)



Therefore,  the ratio under the problem's question is

     =  = .    ANSWER

Solved.

------------

Surely, one can avoid calculating unshaded area (4), when the area of grey part (3) is just calculated.

I did it only for the purpose of completeness.



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