Problem #76

A straight rod is embedded in a solid rectangular block made of translucent plastic. Label three of the faces that meet at a corner A, B, and C. When the sun is directly overhead, face A of the block is placed on level ground. The length of the shadow of the rod is 5 units. When face B is placed on the ground the shadow's length is 6 units and when the face C is placed on the ground, the shadow's length is 7 units.

How long is the rod?

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