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Unattainable Perimeters

Source: 2015 AMC 12A #2

February 4, 2015
geometryperimeterinequalitiestriangle inequalityAMC

Problem Statement

Two of the three sides of a triangle are 2020 and 1515. Which of the following numbers is not a possible perimeter of the triangle?
<spanclass=latexbold>(A)</span>52<spanclass=latexbold>(B)</span>57<spanclass=latexbold>(C)</span>62<spanclass=latexbold>(D)</span>67<spanclass=latexbold>(E)</span>72<span class='latex-bold'>(A) </span>52\qquad<span class='latex-bold'>(B) </span>57\qquad<span class='latex-bold'>(C) </span>62\qquad<span class='latex-bold'>(D) </span>67\qquad<span class='latex-bold'>(E) </span>72