MathDB
2022 B Individual #24

Source:

April 30, 2022
2022 B Individual

Problem Statement

Jenn draws a scalene triangle, and measures the heights from each of the vertices to its opposite side. She discovers that the three height lengths are all roots of the polynomial x33.9x2+4.4x1.2.x^3 - 3.9 x^2 + 4.4 x - 1.2. What is the length of the inradius of the triangle?
<spanclass=latexbold>(A)</span>313<spanclass=latexbold>(B)</span>311<spanclass=latexbold>(C)</span>27<spanclass=latexbold>(D)</span>815<spanclass=latexbold>(E)</span>914<span class='latex-bold'>(A) </span>\frac{3}{13}\qquad<span class='latex-bold'>(B) </span>\frac{3}{11}\qquad<span class='latex-bold'>(C) </span>\frac{2}{7}\qquad<span class='latex-bold'>(D) </span>\frac{8}{15}\qquad<span class='latex-bold'>(E) </span>\frac{9}{14}