Find the length of the perpendicular to the base of this equilateral triangle.

Geometry Level 2

ABCABC is an equilateral triangle with side length 1. Square DEFGDEFG is placed in triangle ABCABC such that points E,E, F,F, and GG are on segments AB,AB, BC,BC, and CA,CA, respectively.

What is the length of the perpendicular from point DD to segment BC?BC?

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