# 2006 AMC 8 Problems/Problem 10

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

## Problem

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?

$\textbf{(A)}$ $[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((1,12)); dot((2,6)); dot((3,4)); dot((4,3)); dot((6,2)); dot((12,1)); label("l", (0,6), W); label("w", (6,0), S);[/asy]$

$\textbf{(B)}$ $[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((1,1)); dot((3,3)); dot((5,5)); dot((7,7)); dot((9,9)); dot((11,11)); label("l", (0,6), W); label("w", (6,0), S);[/asy]$

$\textbf{(C)}$ $[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((1,11)); dot((3,9)); dot((5,7)); dot((7,5)); dot((9,3)); dot((11,1)); label("l", (0,6), W); label("w", (6,0), S);[/asy]$

$\textbf{(D)}$ $[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((1,6)); dot((3,6)); dot((5,6)); dot((7,6)); dot((9,6)); dot((11,6)); label("l", (0,6), W); label("w", (6,0), S);[/asy]$

$\textbf{(E)}$ $[asy] size(75); draw((0,-1)--(0,13)); draw((-1,0)--(13,0)); dot((6,1)); dot((6,3)); dot((6,5)); dot((6,7)); dot((6,9)); dot((6,11)); label("l", (0,6), W); label("w", (6,0), S);[/asy]$

## Solution

The length of the rectangle will relate invertly to the width, specifically using the theorem $l=\frac{12}{w}$. The only graph that could represent a inverted relationship is $\boxed{\textbf{(A)}}$. (The rest are linear graphs that represent direct relationships, therefore they are incorrect.)