MathDB
Triangle Algebra

Source: 2014 AMC 12B #13

March 2, 2014
geometryAMC

Problem Statement

Real numbers aa and bb are chosen with 1<a<b1<a<b such that no triangle with positive area has side lengths 1,a,1,a, and bb or 1b,1a,\tfrac{1}{b}, \tfrac{1}{a}, and 11. What is the smallest possible value of bb?
<spanclass=′latex−bold′>(A)</span> 3+32<spanclass=′latex−bold′>(B)</span> 52<spanclass=′latex−bold′>(C)</span> 3+52<spanclass=′latex−bold′>(D)</span> 3+62<spanclass=′latex−bold′>(E)</span> 3{ <span class='latex-bold'>(A)</span>\ \dfrac{3+\sqrt{3}}{2}\qquad<span class='latex-bold'>(B)</span>\ \dfrac52\qquad<span class='latex-bold'>(C)</span>\ \dfrac{3+\sqrt{5}}{2}\qquad<span class='latex-bold'>(D)</span>}\ \dfrac{3+\sqrt{6}}{2}\qquad<span class='latex-bold'>(E)</span>\ 3
Back to ProblemsView on AoPS