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Scott

[Puzzle] #176 - purple - The Lake

**Posted:** Tue Jul 12, 2005 8:15 pm

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Perplex City is a game whose only rule is: There must be a party.
Balance of Powers is a game whose only rule is: There must be a political party.

Scott

**Posted:** Tue Jul 12, 2005 8:45 pm

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Perplex City is a game whose only rule is: There must be a party.
Balance of Powers is a game whose only rule is: There must be a political party.

alaranth

There's an answer and method of solving here for those who are Google-inclined. Wink

**Posted:** Tue Jul 12, 2005 8:46 pm

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* PFCMacWalker > grope: !attach Alaranth
<Alaranth> kinky
<PFCMacWalker> success
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<Cns_strifey> So I technically enhottenated Alaranth?

RI_Barnica · Veteran Joined: 01 Nov 2004 Posts: 124

Seems like I could've eventually got this one, but I'm too lazy. As this is represented as a classic puzzle, I ran a google image search on Sam Loyd. Sure enough, A solution is available here.

**Posted:** Tue Jul 12, 2005 8:47 pm

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"The mad fishmonger of Worcester shovels his periwinkles everywhere. " -Charles Fort

neophoenix

**Posted:** Sat Aug 13, 2005 2:43 am

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neophoenix� │ 023/100 Scarlett's card distribution challenge
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Guest · Guest

As an additional note, one of Sam Loyd's famous classical problems was the "Plato's Cubes". Funny coincidence Smile

.

http://www.cut-the-knot.org/pythagoras/Plato.shtml

**Posted:** Sat Aug 13, 2005 3:41 am

predominant · Kilroy Joined: 13 Aug 2005 Posts: 1

SPAM DELETED -Brian Censored

**Posted:** Fri Aug 19, 2005 1:12 pm

michalis12 · Kilroy Joined: 25 Nov 2005 Posts: 1

Right,

Anyone interested in the solution read along...
The lake, which is a triangle, has three sides that are known to us. Let's say A, B and C.

A= Square root of 74
B= Square root of 116
C= Square root of 370

According to Heron's formula the Area of the triangle when all 3 sides are known can be derived from the formula:

ABC= Square root of [S(S-A)(S-B)(S-C)]

where S= (A+B+C)/2

In our case we have
A= 8.602325267
B= 10.77032961
C= 19.23538406

Hence,
S=19.30401947
Replacing S, A, B and C in the formula we get the area of the triangle

Area of ABC= 11

**Posted:** Fri Nov 25, 2005 9:58 pm

Juxta · Unfettered Joined: 28 Aug 2005 Posts: 675

Hi Michalis, any chance that you could add spoiler tags to your answer please, for the unwary browser amongst us? Smile

If you aren't sure how to do it, just use [ spoiler ] before the text and [ /spoiler ] afterwards - removing the spaces.

J

**Posted:** Sat Nov 26, 2005 8:11 am

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