Amusements in Mathematics HTML version

This puzzle is not difficult, but it will be found entertaining to discover the simple rule
for its solution. I have a rectangular cardboard box. The top has an area of 120 square
inches, the side 96 square inches, and the end 80 square inches. What are the exact
dimensions of the box?
Two men broke into a church tower one night to steal the bell-ropes. The two ropes
passed through holes in the wooden ceiling high above them, and they lost no time in
climbing to the top. Then one man drew his knife and cut the rope above his head, in
consequence of which he fell to the floor and was badly injured. His fellow-thief called
out that it served him right for being such a fool. He said that he should have done as he
was doing, upon which he cut the rope below the place at which he held on. Then, to his
dismay, he found that he was in no better plight, for, after hanging on as long as his
strength lasted, he was compelled to let go and fall beside his comrade. Here they were
both found the next morning with their limbs broken. How far did they fall? One of the
ropes when they found it was just touching the floor, and when you pulled the end to the
wall, keeping the rope taut, it touched a point just three inches above the floor, and the
wall was four feet from the rope when it hung at rest. How long was the rope from floor
to ceiling?
Readers will recognize the diagram as a familiar friend of their youth. A man possessed a
square-shaped estate. He bequeathed to his widow the quarter of it that is shaded off. The
remainder was to be divided equitably amongst his four sons, so that each should receive
land of exactly the same area and exactly similar in shape. We are shown how this was
done. But the remainder of the story is not so generally known. In the centre of the estate
was a well, indicated by the dark spot, and Benjamin, Charles, and David complained that
the division was not "equitable," since Alfred had access to this well, while they could
not reach it without trespassing on somebody else's land. The puzzle is to show how the
estate is to be apportioned so that each son shall have land of the same shape and area,
and each have access to the well without going off his own land.
As I sat in a railway carriage I noticed at the other end of the compartment a worthy
squire, whom I knew by sight, engaged in conversation with another passenger, who was
evidently a friend of his.
"How far have you to drive to your place from the railway station?" asked the stranger.