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

by : $134$

 * A Fence Problem

Solution
$35$ feet.

Proof

 * Dudeney-Modern-Puzzles-134-solution.png

Let $x$ be the distance required.

Let $y$ be the distance marked on the diagram.

We have:

The above leads to a quartic equation which is irksome to solve.

However, we are told that $x$ is an exact number of feet.

We have that $91^2$ is the sum of two square numbers in exactly one way:

Inserting $x = 35$ and $y = 84$ into $2$ proves that these numbers are consistent with the premises.

Hence the result.