A plank of wood has one end, A, against a vertical wall. Its other end, B, is on horizontal ground. When end A slips down 8cm, end B moves 4cm further away from the wall.
When end A slips down a further 9cm, end B moves a further 3cm away from the wall. Find the length of the plank.
Let the original distances from A and B to the corner where the ground meets the wall be a cm and b cm, respectively.
Then, using Pythagoras’ theorem,we have
a2 + b2 = (a − 8)2 + (b + 4)2 = (a − 17)2 + (b + 7)2
After simplification, this produces the equations below.
2a − b = 10
17a − 7b = 169
Solving these, we obtain a = 33 and b = 56. The length of the plank is then 65 cm.
This problem relies on three Pythagorean triples(3, 4, 5), (5, 12, 13) and (33, 56, 65) where the first two are scaled up to give the same hypotenuse.
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