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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bobbym
2013-07-11 08:08:40

Over at Brilliant - AOPS they say "Work smarter, not harder." But where does that leave guys like me?

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
2013-07-11 08:02:22

yes, yours was correct

bobbym
2013-07-11 06:40:06

Hi cooljackiec;

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?

cooljackiec
2013-07-11 04:49:45

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

bob bundy
2013-07-10 17:28:44

hi cooljackiec,

(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  smile

Bob

bobbym
2013-07-10 09:19:26

Hi cooljackiec;

cooljackiec
2013-07-10 08:16:23

Let  ABCDEFGH be a rectangular prism, as shown. The areas of faces ABCD, ABFE, and ADHE  are 56, 110, and 385, respectively. Find the volume of the rectangular prism.

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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