MathDB
Triangle equality and obtuse triangle problem

Source: AHSME 1995 #23

November 21, 2005
inequalitiescalculusintegrationtrigonometrytriangle inequalityPythagorean Theoremgeometry

Problem Statement

The sides of a triangle have lengths 1111,1515, and kk, where kk is an integer. For how many values of kk is the triangle obtuse?
<spanclass=latexbold>(A)</span> 5<spanclass=latexbold>(B)</span> 7<spanclass=latexbold>(C)</span> 12<spanclass=latexbold>(D)</span> 13<spanclass=latexbold>(E)</span> 14<span class='latex-bold'>(A)</span>\ 5 \qquad <span class='latex-bold'>(B)</span>\ 7 \qquad <span class='latex-bold'>(C)</span>\ 12 \qquad <span class='latex-bold'>(D)</span>\ 13 \qquad <span class='latex-bold'>(E)</span>\ 14