MathDB
Apothem of a Square

Source:

February 1, 2009
geometryperimeterLaTeX

Problem Statement

The apothem of a square having its area numerically equal to its perimeter is compared with the apothem of an equilateral triangle having its area numerically equal to its perimeter. The first apothem will be: <spanclass=latexbold>(A)</span> equal to the second<spanclass=latexbold>(B)</span> 43 times the second<spanclass=latexbold>(C)</span> 23 times the second<spanclass=latexbold>(D)</span> 23 times the second<spanclass=latexbold>(E)</span> indeterminately related to the second <span class='latex-bold'>(A)</span>\ \text{equal to the second} \qquad<span class='latex-bold'>(B)</span>\ \frac {4}{3} \text{ times the second} \qquad<span class='latex-bold'>(C)</span>\ \frac {2}{\sqrt {3}} \text{ times the second} \\ <span class='latex-bold'>(D)</span>\ \frac {\sqrt {2}}{\sqrt {3}} \text{ times the second} \qquad<span class='latex-bold'>(E)</span>\ \text{indeterminately related to the second} [Note: The apothem of a regular polygon is a line segment from the center to the midpoint of one of its sides.]