MathLabs

Problem 2

Prove that if one and only one edge of a tetrahedron is greater than 11, then its volume is at most 18\frac18.
Step 1 of 6: Name the long edge
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AB>1,AC,AD,BC,BD,CD≤1AB>1,\quad AC,AD,BC,BD,CD\le 1
Detailed analysis

Call the only edge longer than 11 by AB, and put z=CDz=CD. Then 0<z≤10<z\le1.