Wednesday, May 14, 2014

Mystery Challenge Number 1

Mystery Challenge Number #1

A priceless sword with associations to Mary, Queen of Scots had been stolen from an estate, and Max had agreed to lend his teams services on the matter. The local constabulary was making much of the thief's escape, and sought to ascertain which of the nearby villages was the closest-Shenstone, Rushock, or Chaddesley.

The sword's custodian expressed his opinion that it seemed as if all three were as far away as each other, although he had never actually attempted to measure the distances involved. The sergeant maintained that the exact distance was important to know.

It was known that the distance from Shenstone to Caddesley was one and a half miles, from Shenstone to Rushock was one and three tenths miles, and from Rushock to Chaddesley was one and two fifths miles.

Can you discern the distance from the estate to the villages?


Given the distances between the villages, the application of Pythagoras' theorem will quickly establish the height of the triangle they form, treating any one of the lines as the base. If Rushock to Chaddesley is the base, the height of the triangle to Shenstone is one and one fifth miles. This makes the area of the triangle twenty-one twenty-fifths of a square mile. Then multiply the three sides together and divide by four times the area to get the distance to the central spot, and you'll discover that the distance is thirteen sixteenths of a mile.

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