Problem
2006 AMC 8 Problem 10
Jorge's teacher asks him to plot all the ordered pairs (w, l) of positive integers for which w is the width and l is the length of a rectangle with area 12. What should his graph look like?
\textbf{(A)} ![[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((1,12)); dot((2,6)); dot((3,4)); dot((4,3)); dot((6,2)); dot((12,1)); label("$l$", (0,6), W); label("$w$", (6,0), S);[/asy]](/static/aops/3a01c402526b29bd19717ac27a964c97c7c90256.png)
\textbf{(B)} ![[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((1,1)); dot((3,3)); dot((5,5)); dot((7,7)); dot((9,9)); dot((11,11)); label("$l$", (0,6), W); label("$w$", (6,0), S);[/asy]](/static/aops/5bac0fbc6b424579dd878f2c9b6fd25e5fdc57bc.png)
\textbf{(C)} ![[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((1,11)); dot((3,9)); dot((5,7)); dot((7,5)); dot((9,3)); dot((11,1)); label("$l$", (0,6), W); label("$w$", (6,0), S);[/asy]](/static/aops/d16c6eb0a4feae2b575a49deae60ef5f2dc24924.png)
\textbf{(D)} ![[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((1,6)); dot((3,6)); dot((5,6)); dot((7,6)); dot((9,6)); dot((11,6)); label("$l$", (0,6), W); label("$w$", (6,0), S);[/asy]](/static/aops/7822b4158ccde67dd21fb1750f181c9088a739f2.png)
\textbf{(E)} ![[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((6,1)); dot((6,3)); dot((6,5)); dot((6,7)); dot((6,9)); dot((6,11)); label("$l$", (0,6), W); label("$w$", (6,0), S);[/asy]](/static/aops/286b49157b5fb1c448956dfccefe8e5ad2ff0cce.png)
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