## Setting up some equations

Let x and y represent the distances as labelled on the figure.

Then similar triangles gives

Also, the Pythagorean relationship gives

So we have a system of two equations in two variables and we can graph them on the same axes. The first is a rectangular hyperbola and the second is a circle.

Only the first quadrant is of interest. Why?

Now, solve:

Return to the **Ladder and Box Problem**