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

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

- Mr. Grindle's Garden

*"My neighbour," said Mr. Grindle, "generously offered me, for a garden,*

*"And what was the largest area you were able to enclose?" asked his friend.*

*Perhaps the reader can discover Mr. Grindle's correct answer.*

## 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 | |||||||||||

\(\ds \) | \(=\) | \(\ds \sqrt {5040}\) | ||||||||||||

\(\ds \) | \(\approx\) | \(\ds 70.99\) |

$\blacksquare$

## Sources

- 1926: Henry Ernest Dudeney:
*Modern Puzzles*... (previous) ... (next): Solutions: $130$. -- Mr. Grindle's Garden - 1968: Henry Ernest Dudeney:
*536 Puzzles & Curious Problems*... (previous) ... (next): Answers: $260$. Mr. Grindle's Garden