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A man and his dog. An investigation

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A man and his dog breadth length field A B Each day a man takes his dog out for a walk. They walk along the side of a field from point A to point B. The length of the field is 20 metres more than the breadth.

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One day the man notices that a path has been made diagonally across the field. If he takes this route instead of going round the sides of the field he finds that his walk is 30 metres shorter. breadth length path A B Use the above information to find the dimensions of the field.

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Solution:-A man and his dog: Let a = breadth and then the length is a + 20. Using Pythagoras you obtain the equation = = This expands and simplifies to give which solves using the quadratic formula to give ‘a’ as 43.45 meters.

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EXAMPLE 3 Use the quadratic formula y = 10x 2 – 94x + 3900 4200 = 10x 2 – 94x – 3900 0 = 10x 2 – 94x – 300 Write function. Substitute 4200 for y. Write.

EXAMPLE 3 Use the quadratic formula y = 10x 2 – 94x + 3900 4200 = 10x 2 – 94x – 3900 0 = 10x 2 – 94x – 300 Write function. Substitute 4200 for y. Write.

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