length of the yellow line

Geometry Level 3

Four squares of respective side lengths 4, 9,15, and 21 are arranged as shown. Find the length of the yellow line. If your answer can be expressed as a7+b7c\frac{a}{7}+\frac{b}{7}\sqrt{c}, where cc is square free, give a+b+c.a+b+c.

Note: Neglect the thickness of the lines.

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