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#1 Re: Help Me ! » Finding the area using Pythagoras » 2010-12-28 12:44:50

Thanks again to you both for your superb help and perseverance. I must admit I was very pleasantly surprised at the obvious enjoyment and passion the both of you feel for math (and for helping others appreciate the beauty of math), and want to let you know I think you are both a credit to the community.

Thanks again for all your help, and all the best in the New Year.
Kind regards,

#2 Re: Help Me ! » Finding the area using Pythagoras » 2010-12-26 22:48:18

Hi Bobbym and Bob Bundy;

Mr. Bundy's latest solution is quite elegant and satisfying, and the one I like the best (and can understand).

Bobbym, regarding solving for "13 x^2-13120 x =-3200000", I can do this using the equation to solve for the roots of a quadratic (I get X=596.7 and X=412.5 as 2 solutions), but your offer to help me solve quadratics was lovely and very gracious. Thank you.

I can't tell you how much I appreciate the amount of time and effort you have both spent trying to help out with this. I think I agree with Mr. Bundy that this is far from a ridiculously simple problem (all the other examples in this section of the grade 8 math book were just that - ridiculously simple, and I thought I was simply missing something obvious for this problem). I too am too stupid to give up, but I must add that I am often too stupid to know when to give up as well (this was a problem that I thought I could solve in 2-3 minutes but has eaten up a good portion of the holidays. I even dreamed about it at one point!).

Yes, some problems cannot be easily solved with pen and paper, but I cannot understand why such an example was given in a grade 8 math book (especially as none of the other examples needed anything more than a calculator).

Thanks again to you both for all your help. It is hugely appreciated, and I wish you all the best in the New Year. As for sprouts, the less said the better I think.

With best wishes,

#3 Re: Help Me ! » Finding the area using Pythagoras » 2010-12-25 13:50:03

Hi Bobbym and Bob Bundy;

Thank you both for your help and patience in this. Unfortunately I am still unable to solve the problem, even with the help and advice proffered.

[By the way, the background to this problem is that it was presented in a math book aimed at grade 8 students, so I am somewhat surprised at the complexity of the answer and the need for such heavy computation]

Bobbym, I can understand your math and logic up to the point where you write "You can eliminate x and after some algebra", as it is from here on in that I am lost. How does one eliminate x, and what is the algebra involved (I cannot generate the next 3 equations you list). Also, I was unsure what you meant by "Can you finish now with the top equation?" Which is the top equation (the one with the y^4 term in it or the one starting with 800z=)?

Mr. Bundy, I'm sorry but I don't even understand your basic premise (eg "let 2s = a + b + c"; why 2s?) and I could not decipher your response (even though your answer is correct).

I'm sorry if I appear thick but both your answers do not make sense to me. Perhaps this is beyond me (although I am still surprised that someone obviously thought a grade 8 student could solve this without the help of a computer), and I wouldn't be offended if either of you gave up on me.

I did want to express my thanks and appreciation for your help thus far, and I am still interested in how to get the final answer if this is possible without extensive computing power!

Kind regards,

#4 Re: Help Me ! » Finding the area using Pythagoras » 2010-12-24 23:44:09

Hi Bobbym;

Thanks for your reply and your solution. Your answer is correct but I still cannot figure out how you arrived at it. Your simultaneous equations all make sense (they are in fact the same ones I derived), but when I tried to solve them I got stuck. I could not figure out what you meant by “Solve by using the equation that only has x's in it first” (equation number 3 in your list), as when I solve it all I get is either x^2 = x^2 or 50=50. Also, by “The z variable can be expressed in terms of x also” I assume you mean z=x+y-w but I did not see how that helps.

I really appreciate your taking the time to respond and I feel I am close but I am still not quite there. Any more details would be greatly appreciated.

Kind regards,

#5 Help Me ! » Finding the area using Pythagoras » 2010-12-23 21:09:29

Replies: 25


I am trying to solve what must be a ridiculously simple problem involving Pythagoras’ theorem and some simple geometry but I seem to be missing something. The problem is this:

A farmer has a square field and has set up a drinking trough at a point in the middle of the field that is 50m from one corner of the field, 30m from another corner, and 40m from a third corner (the diagram shows the configuration). The goal is to find the size of the field (either the area of the length of one side – it is a square field).

Note that the 30m and 50m lines do not make the diagonal line of the square field.

I have constructed several right angled triangles and looked for common sides to try and solve simultaneous equations but I end up with 3 equations and 4 unknowns and am thus unable to solve this. 

Any help (especially in the form of a detailed explanation) would be greatly appreciated. By the way, I am not a student with a homework assignment – this is a problem I came across and am embarrassed that at my age I cannot figure it out!

Kind regards,

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