A square island is surrounded by a square deep moat (10m wide, 14.5m at corner). Two planks (9.5m long) ar?

Question

A square island is surrounded by a square deep moat (10m wide, 14.5m at corner). Two planks (9.5m long) are available to cross the moat but together they are 5 m too short if laid end to end. How can the moat be crossed safely with no nails or rope available?

Answer 1

The best way to show this is to draw it out following these instructions.

Draw the configuration as nine tiles in a grid with each tile 10m on a side and the centre tile being the island. Something like

XXX
XOX
XXX

This shows you that the distance between the corner of the island Y and the corner of the moat X is the hypotenuse of a right angled triangle with two equal sides of 10m.
Using Pythagoras, we get the size of this hypotenuse as
sqrt(10*10 + 10*10) = sqrt(200) is approx 14.5 - the number we're given.
If we lay one of the 9.5 metre planks over the corner of the moat this forms another triangle (hypotenuse in the opposite direction from the one we've just looked at). We know that since the plank is 9.5m, the hypotenuse of this triangle is 9.5m. If we take a right angle from the midpoint of the plank to the corner of the moat, that gives us another right angled triangle where the distance between the midpoint of the plank and the corner of the moat is equal to half the length of the plank.
Therefore from the corner of the island to the midpoint of the plank = the total distance between corner of island and corner of moat minus half the length of the plank.

= 14.5 - 4.75 = 9.25.

This is less than 9.5m so we can lay the remaining plank from the corner of the island to the middle of the plank (with .25m to spare)

Answer 2

Lay one plank across one corner, such that its length forms the hypotenuse of a right angled triangle of equal height and base.

9.5^2 = 2(x^2) where x is the length of the two other sides.

The distance from the corner to the midpoint of this plank can be found using simple trigonometry.

Following this, lay the second plank with one end at the midpoint of the first, and the second at the corner of the island. Easy!

Hope this helps!

Answer 3

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Answer 4

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