Online Geometry
Problem 748: Quadrilateral, 90 Degrees, Diagonal, Perpendicular,
Metric Relations. Level: High School, Honors Geometry, College,
Mathematics Education

The figure shows a quadrilateral ABCD with
angle B = angle D = 90 degrees. AB and DC meet at E, AD and BC meet at
F. EG, CH, AM, and FN are perpendicular to
diagonal BD. If EG = 3, AM =4, and FN =7, find GH.