A woman starts at a point A. She wlaks due east for 300m and then due north for 400m, ending at B. Sketch her path, and sketch the shortest path between A and B. What is the shortest distance from A to B?

Acceptable Solution:

Sketch path of woman, shortest path. Find shortest distance.

\begin{figure} \epsfig {file=ex5a.eps, width = 0.3\textwidth}\end{figure}

Let $x$ = shortest distance between A and B. Using the distance formula,


\begin{displaymath}\begin{array}{ccl} x & = & \sqrt{(300)^2 + (400)^2}\\ & = & \sqrt{250,000}\\ & = & \fbox {500m}\end{array}\end{displaymath}

Unacceptable Solution:

Sketch path of woman, shortest path. Find shortest distance.

\begin{figure} \epsfig {file=ex5u.eps, width = 0.3\textwidth}\end{figure}


\begin{displaymath}\begin{array}{ccl} x & = & \sqrt{(300)^2 + (400)^2}\\ & = & \sqrt{250,000}\\ & = & \fbox {500}\end{array}\end{displaymath}

(There has been no statement of what $x$ represents, and there have not been any use of units in either the figure or the final answer.)