1. Subscribervenda
    Dave
    S.Yorks.England
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    28 Feb '22 15:11
    @ponderable said
    Seems that I got the wording right.
    Well done Pondy
    That is correct
  2. Joined
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    15 Apr '22 14:211 edit
    Do you have any more?
  3. Subscribervenda
    Dave
    S.Yorks.England
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    09 May '22 13:06
    A fort is a convex polygon 700m in perimeter.Patrols walk around the fort staying exactly 10m from it's walls.How far does the patrol walk in one circuit ?
    Good luck.I don't even know what a convex polygon is!
    My first question would be are they walking inside or outside,but as the question doesn't say,I suspect it doesn't matter!
  4. Joined
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    09 May '22 13:26
    @venda said
    A fort is a convex polygon 700m in perimeter.Patrols walk around the fort staying exactly 10m from it's walls.How far does the patrol walk in one circuit ?
    Good luck.I don't even know what a convex polygon is!
    My first question would be are they walking inside or outside,but as the question doesn't say,I suspect it doesn't matter!
    If it were inside, the question wouldn't be answerable. (Consider a fort 10m wide and 70m long...)

    (A convex polygon, by the way, is a rectangle, or a triangle, or any multi-lined shape with only external angles. A star, for instance, is not one - it has some reflex angles and is therefore concave.)

    Anyway, the answer is Reveal Hidden Content
    762.83 and a bit metres
    .
    That's because, if you make a picture, you wil see that Reveal Hidden Content
    they always walk along the sides for exactly the distance of that side. Those parts, therefore, add up to 700 as well. And when they get to a corner, they have to turn through a circle segment until they can start walking along the next side. But, because the fort is convex, and they end up back at the starting point for the next circuit, all those segments fit together to make exactly one circle of radius 10 - a length of 2 × pi × 10 = 62.83 plus change.
  5. Subscribervenda
    Dave
    S.Yorks.England
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    09 May '22 14:12
    The paper doesn't give a numerical answer but there is an explanation:-
    Reveal Hidden Content
    (700 + 20pi)m - My computer doesn't have the pi symbol
    The path proceeds in straight lines that are parallel and equal in length to the walls interleaved with arcs of a circle 10m in radius.The arcs combine to make a full circle

    Way beyond me I'm afraid.
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    09 May '22 14:17
    @venda said
    The paper doesn't give a numerical answer but there is an explanation:-
    Hidden content removed
    Way beyond me I'm afraid.
    Draw it. Start by looking up what a convex polygon is, draw some (start with a rectangle, it's easiest to think about), then draw how you would walk a fixed distance around it. It's easier to see than to talk about.
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