If the slant height of a triangular pyramid is 12 and the lateral edge is 15, then what is the height and the base edge length?
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The slant height is the perpendicular bisector of a lateral face (perpendicular from the vertex of the pyramid to the midpoint of the base edge). So the lateral edge, slant height and half the base edge form a right triangle.

The half-edge length=√(15²-12²)=√(225-144)=√81=9.

The base edge=2×9=18.

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