# Henry Ernest Dudeney/Modern Puzzles/130 - Mr. Grindle's Garden/Solution/Proof 1

## Modern Puzzles by Henry Ernest Dudeney: $130$

Mr. Grindle's Garden
"My neighbour," said Mr. Grindle, "generously offered me, for a garden,
as much land as I could enclose with four straight walls measuring $7$, $8$, $9$ and $10$ rods in length respectively."
"And what was the largest area you were able to enclose?" asked his friend.

## Solution

Just under $71$ square rods.

## Proof

Let $\AA$ square rods be the area of the garden.

We are given that $\AA$ is the greatest possible for the given sides.

We also have that the sides of the garden are in arithmetic sequence.

Thus:

 $\ds \AA$ $=$ $\ds \sqrt {7 \times 8 \times 9 \times 10}$ Greatest Area of Quadrilateral with Sides in Arithmetic Sequence $\ds$ $=$ $\ds \sqrt {5040}$ $\ds$ $\approx$ $\ds 70.99$

$\blacksquare$