I kept this problem on 'subscription', as I was hopeful of coming up with a grade 9 solution using Pythagoras.

Here it is.

Set up a spreadsheet with 'w' as a variable.

use formulas to compute

y = root(30*30 - w*w)

x = root(40*40-y*y)

z = root(50*50-x*x)

Compute w + x - y - z. For a square this value should be zero.

Use goal seek to 'find' a value of zero by varying w.

The screen shot from Excel shows the formula set up and the goal seek command with the finished values.

I have used goal seek with this age of child so I think it is a valid method.

Sorry it has taken so long to dream it up.

Bob

]]>I think you are both a credit to the community.

MIF wrote:

I second that!

I was going to rant on and on about how that comment does not apply to me. I always get more out of answering any question then I give to the OP. So actually, in my case it is total selfishness. It is impossible to do a selfless act. What was I going to say? Oh, yea, since MIF has seconded it I cannot rant about it.

]]>Thank you for that comment. I still have the brain cells working on this. My Sketchpad files are up to version 7 now. I'm hoping there's a 'straight pythag. with 1 variable' solution lurking in there somewhere.

Happy New Year!

Bob

]]>Thanks again for all your help, and all the best in the New Year.

Kind regards,

Tonia

Yes, that person knew I would not know what it means.

]]> someone wrote:

sesquipedalian

I had to look that up. Perhaps it was a very subtle joke.

Happy New Year!

Bob

]]>That's very gracious of you.

I have to quote that in contrast to the usual comments I get. I have been called boring, annoying, dishonorable, sesquipedalian, idiotic, sickening, rude, pathetic, cheesy, creepy, arrogant, a big blowhard, bad at math, messy, incomprehensible, bad at german, bad at chess, bad at computers, despicable, unimaginative, retarded, dishonest, a lizard and a lowdown punk. That is just from the girls.

Yes, Math is Fun!

]]>That's very gracious of you. I keep coming back to (30,40,50) as a Pythagorean Triple. Surely that triangle crops up somewhere, but I have't found it yet.

Oh, yes, Tonia; it's just occurred to me: Maths Is Fun apparently.

Bob

]]>Very impressed by this, bobbym. That's got to be the best method so far. :):)

Tonia wrote:

I appreciate the amount of time and effort you have both spent trying to help out with this.

You are very welcome. I have enjoyed trying the problem and haven't given up on finding the 'grade 8' solution.

Watch this space!

Bob

]]>Hold the presses! I did it!

Subtract the 2 nd equation from the first.

Subtract the 3 rd equation from the second.

Eliminate x and z in equations 6 and 7 using equations 4 and 5.

Solve for y and w in A and B.

That is the trick 2 variables are expressed in terms of S!

Use equation 3 because it uses w and y.

Times by 4S^2

Now you should know how to do this from an earlier post.

Just paper, pen and pythagoras, maybe too hard for an 8th grader. I would not take a chance and say too hard for every 8th grader..

]]>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,

Tonia

Sorry, for the no reply but my internet provider has been going out for large portions of the last 3 days. They are claiming that a bunch of nasty aliens have vandalized their satellite. I think they just have junky lines.

(bobbym, now I look more closely at this I'm stuck also as to how the step *** works as there are some terms with w and z rather than w^2 and z^2. This approach is tough for those of us who don't have Mathematica.)

( Original comments deleted see post below )

Thanks for the sprouts!

]]>How about this method:

See diagram below.

The square ABCD is rotated 90 around B, to give ABA'D'.

E' is the rotated point for E.

Join EE'.

EB = E'B = 40. and angle EBE' = 90

So EBE' is isosceles with angle E'EB = 45 and E'E = 56.6 (by Pythag)

AE' = CE = 30 so use cosine rule to calculate angle AEE' (dash removed in next two lines as it gives an error)

so

Now use cosine rule on triangle AEB

so

Bob

]]>