Arthur Ashe wrote:

Paralysis by analysis.

I say, take thinking out of the solution, it only gets you into trouble. Do not follow Karl Maldens advice, I say leave your brain at home, travel light!

Turn everything into a small template of computational problems and then work on those. The true "Teakettle Principle!"

]]>cooljackiec wrote:

hmmm... i used some weird guessing/intuition and got half of the correct answer of number 1...

That is how I get all my answers. Did you check the answer?

]]>(i) The tetrahedron. I think the little one has sides that are half the large one. So that should fix the ratio of volumes.

LATER EDIT: I've changed my mind about this one. See post 10 on

http://www.mathisfunforum.com/viewtopic … 60#p277760

(ii) If you call the sides a, b and c then

ab = 56 ........................(p)

bc = 110 ........................(q)

ca = 385 .........................(r)

If you do equation (p) divide by (q) you'll eliminate b

Then make a the subject and substitute into (r) to solve for c.

Then you can substitute back to get a and b.

(iii) Again call the sides a, b and c.

From the information given

This time you cannot solve for a, b and c because there are only two equations. But you don't need to, because we only want to get

There's a neat way to get this. Start with

If you substitute in the values you know you'll be left with the value of a^2 + b^2 + c^2

Bob

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The total area of all the faces of a rectangular prism is 22, and the total length of all its edges is 24. Find the length of the internal diagonal of the prism.

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