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Tetrahedron Problem

Source: 1992 National High School Mathematics League, Exam One, Problem 3

February 26, 2020
geometry3D geometrytetrahedron

Problem Statement

Areas of four surfaces of a tetrahedron are S1,S2,S3,S4S_1,S_2,S_3,S_4. And the largest one of them is SS. λ=S1+S2+S3+S4S\lambda=\frac{S_1+S_2+S_3+S_4}{S}, then λ\lambda always satisfies (A)2<λ≤4(B)3<λ<4(C)2.5<λ≤4.5(D)3.5<λ<5.5\text{(A)}2<\lambda\leq4\qquad\text{(B)}3<\lambda<4\qquad\text{(C)}2.5<\lambda\leq4.5\qquad\text{(D)}3.5<\lambda<5.5
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