Problem of the Week Problem C
Locate the Fourth Vertex
Quadrilateral BDFH is constructed so that each vertex is on a different side of
square ACEG. Vertex B is on side AC so that AB = 4 cm and BC = 6 cm.
Vertex F is on EG so that EF = 3 cm and FG = 7 cm. Vertex H is on GA so
that GH = 4 cm and HA = 6 cm. The area of quadrilateral BDFH is 47 cm2.
The fourth vertex of quadrilateral BDFH, labelled D, is located on side CE so
that the lengths of CD and DE are both positive integers.
Determine the lengths of CD and DE.