MathDB

11

Part of 2003 AMC 12-AHSME

Problems(2)

Square and Equilateral Triangle

Source:

2/17/2008
A square and an equilateral triangle have the same perimeter. Let A A be the area of the circle circumscribed about the square and B B be the area of the circle circumscribed about the triangle. Find A/B A/B. <spanclass=′latex−bold′>(A)</span> 916<spanclass=′latex−bold′>(B)</span> 34<spanclass=′latex−bold′>(C)</span> 2732<spanclass=′latex−bold′>(D)</span> 368<spanclass=′latex−bold′>(E)</span> 1 <span class='latex-bold'>(A)</span>\ \frac{9}{16} \qquad <span class='latex-bold'>(B)</span>\ \frac{3}{4} \qquad <span class='latex-bold'>(C)</span>\ \frac{27}{32} \qquad <span class='latex-bold'>(D)</span>\ \frac{3\sqrt{6}}{8} \qquad <span class='latex-bold'>(E)</span>\ 1
geometryperimeterarea of a triangle
Cassandra's Watch

Source:

1/4/2009
Cassandra sets her watch to the correct time at noon. At the actual time of 1:  ⁣ 00 PM \text{1: \!\,00 PM}, she notices that her watch reads 12:  ⁣ 57 \text{12: \!\,57} and 36 36 seconds. Assuming that her watch loses time at a constant rate, what will be the actual time when her watch first reads 10:  ⁣ 00 PM \text{10: \!\,00 PM}? <spanclass=′latex−bold′>(A)</span> 10:  ⁣ 22 PM and 24 seconds<spanclass=′latex−bold′>(B)</span> 10:  ⁣ 24 PM<spanclass=′latex−bold′>(C)</span> 10:  ⁣ 25 PM <span class='latex-bold'>(A)</span>\ \text{10: \!\,22 PM and 24 seconds} \qquad<span class='latex-bold'>(B)</span>\ \text{10: \!\,24 PM}\qquad<span class='latex-bold'>(C)</span>\ \text{10: \!\,25 PM} <spanclass=′latex−bold′>(D)</span> 10:  ⁣ 27 PM<spanclass=′latex−bold′>(E)</span> 10:  ⁣ 30 PM <span class='latex-bold'>(D)</span>\ \text{10: \!\,27 PM}\qquad<span class='latex-bold'>(E)</span>\ \text{10: \!\,30 PM}