A maths problem that may require A.P.

How to solve this??? A man has 12 iron posts as well as a 4 feet wide iron gate available for the purpose of fencing a semi-circular plot of land. It is understood that the gate needs to be supported by two of the 12 iron posts on either side of the gate. It is also suggested that the remaining posts be spaced equally away from each other. Diameter of plot of land =10m

  1. Deduce where the gate should be placed along the semi-circular pot of land. How to find out the distance between each of the posts.

I know for sure this is an A.P.

Answers
I received your message but I need to fix a software fault - I can't reply on the tutor request form. In the meantime, does the fence have to go all the way round the plot, ie the straight bit as well? And, what do you mean by A.P.?
ianmoth
05 February 2012
it is fenced all the way round de plot...by A.P. i mean arithmetric progression
luke
05 February 2012
Interesting that the gate width is given in feet but the diameter in metres. Presumably you should first decide which to work in. Any preference? Next thing to work out, how far is it all the way round (i.e. the perimeter of this land?
ianmoth
05 February 2012
i wanna work with metres....an is rite round the land, the diamter and de arc of course
luke
05 February 2012
an yes de perimeter of de land
luke
05 February 2012
Assume the gate is straight and therefore needs to be along the straight part of the semi-circle. Total perimeter of semi-circle= pi*5m+10m = 25.708m Let a = length of gate = 4 feet = 1.2192m Given, 12 post (with 2 posts either side of gate). Therefore, using AP we get the following where 'd' is the difference: a+11d=perimeter of semi-circle 1.2192 + 11d = 25.708 Therefore, d = 2.226m
maddiekv
05 February 2012
thanks alot
luke
05 February 2012
Also, do we need to assume that one post must be placed at each end of the diameter? If we don't assume this do we not then "cut off" the corners of the field?
simonwilliams1978
06 February 2012
so help we i tink ur rite we need to assume this
luke
07 February 2012
so how to solve this?
luke
07 February 2012
please help me if i had to assume that i also put a post on each end of the diameter
luke
07 February 2012
and i dont want to fence de gate
luke
07 February 2012
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