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

Modern Puzzles by Henry Ernest Dudeney: $130$

"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.

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

Just under $71$ square rods.

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:

$\ds \AA$

$=$

$\ds \sqrt {7 \times 8 \times 9 \times 10}$

$\ds $

$=$

$\ds \sqrt {5040}$

$\ds $

$\approx$

$\ds 70.99$

$\blacksquare$