Problem:
Tetrahedron ABCD has AB=5,AC=3,BC=4,BD=4,AD=3, and CD=5122. What is the volume of the tetrahedron?
Answer Choices:
A. 32
B. 25
C. 524
D. 33
E. 5242 Solution:
Triangles ABC and ABD are 3-4-5 right triangles with area 6. Let CE be the altitude of △ABC. Then CE=512. Likewise in △ABD, DE=512. Triangle CDE has sides 512,512, and 5122, so it is an isosceles right triangle with right angle CED. Therefore DE is the altitude of the tetrahedron to base ABC. The tetrahedron's volume is 31⋅6⋅512=524.
