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

Modern Puzzles by Henry Ernest Dudeney: $134$

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.

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

Sources

• 1926: Henry Ernest Dudeney: Modern Puzzles ... (previous) ... (next): Geometrical Problems: Various Geometrical Puzzles: $134$. -- A Fence Problem
• 1968: Henry Ernest Dudeney: 536 Puzzles & Curious Problems ... (previous) ... (next): Geometrical Problems: Triangle, Square & Other Polygon Puzzles: $264$. A Fence Problem