Henry Ernest Dudeney/Modern Puzzles/134 - A Fence Problem

by : $134$

 * A Fence Problem
 * This is a problem that is very frequently brought to my notice in various forms.
 * It is generally difficult, but in the form in which I present it it should be easy to the cunning solver.


 * A man has a square field, $60 \ \mathrm {ft.}$ by $60 \ \mathrm {ft.}$, with other property, adjoining the highway.
 * For some reason he put up a straight fence in the line of three trees, as shown,
 * and the length of fence from the middle tree to the tree on the road was just $91$ feet.


 * Dudeney-Modern-Puzzles-134.png


 * What is the distance in exact feet from the middle tree to the gate on the road?