MathDB

24

Part of 2022 MIG

Problems(2)

2022 A Individual #24

Source:

4/28/2022
Cows Alpha and Beta are tied by eight-meter ropes, on the midpoints of adjacent sides of a rectangular fence. Both cows are outside the fence; Alpha can wander in a region with an area of 34π34\pi square meters and Beta can wander in a region with an area of 40π40\pi square meters. What is the area enclosed by the rectangular fence?
<spanclass=′latex−bold′>(A)</span>45<spanclass=′latex−bold′>(B)</span>48<spanclass=′latex−bold′>(C)</span>96<spanclass=′latex−bold′>(D)</span>120<spanclass=′latex−bold′>(E)</span>144<span class='latex-bold'>(A) </span>45\qquad<span class='latex-bold'>(B) </span>48\qquad<span class='latex-bold'>(C) </span>96\qquad<span class='latex-bold'>(D) </span>120\qquad<span class='latex-bold'>(E) </span>144
2022 A Individual
2022 B Individual #24

Source:

4/30/2022
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 x3−3.9x2+4.4x−1.2.x^3 - 3.9 x^2 + 4.4 x - 1.2. What is the length of the inradius of the triangle?
<spanclass=′latex−bold′>(A)</span>313<spanclass=′latex−bold′>(B)</span>311<spanclass=′latex−bold′>(C)</span>27<spanclass=′latex−bold′>(D)</span>815<spanclass=′latex−bold′>(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}
2022 B Individual