"The Rose Garden"

Z

zenith20

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Aug 20, 2010
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a problem from Sh. Devi:

The Rose Garden
In my bungalow in Bangalore I have a beautiful rose garden.
The four sides of the garden are known to be 20, 16, 12 and 10 rods. And it is also known that it has the greatest possible area for those sides,
Can you find the area?
-----------------
Solution:
Half the sum of the side is 29 and from this we deduct the sides in turn, which gives us 9, 13, 17. 19, which when multiplied together make 37791. The square root of this number is 194.4.
194.4 square rods will be the answer
-----------------

i didnt understand the solution, how the GREATEST POSSIBLE AREA has been calculated :(
 
Hello, zenith20!

Where did this problem come from?
And who provided that solution?

The four sides of the my rose garden are known to be 20, 16, 12 and 10 rods.
And it is also known that it has the greatest possible area for those sides,
Can you find the area?

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Solution ??

Half the sum of the side is 29
and from this we deduct the sides in turn, which gives us 9, 13, 17. 19,
which when multiplied together make 37791.
The square root of this number is 194.4.
194.4 square rods will be the answer.

i didn't understand the solution. . Neither did I.
Click to expand...

It seems to have used a "Heron's Formula" for a quadrilateral
. . which automatically produces maximum area.

Even if this is true, it is an extremely obscure theorem to pull out of a hat . . .

 
soroban said:
Hello, zenith20!

Where did this problem come from?
And who provided that solution?
Click to expand...

Dear Sorobon,
Thank you so much for your answer,
this is a puzzle from the book "Puzzles to puzzle you" by shakuntala devi, question no 141, page 91,
and the solution (also by Shakuntala Devi herself) in the same book page 141.

anyway, your idea is really appreciated to me.
thanks again,
Zenith
 
Thanks for this great subject. i've never heard of it, Thank you dear Subhotosh Khan :)
 


From the Wikipedia page: "A triangle may be regarded as a quadrilateral with one side of length zero."

I've never heard of that before; I've always thought that a triangle has infinite sides, with all but three sides having zero length. :wink:

 
Re:

mmm4444bot said:


From the Wikipedia page: "A triangle may be regarded as a quadrilateral with one side of length zero."

I've never heard of that before; I've always thought that a triangle has infinite sides, with all but three sides having zero length. :wink:

Click to expand...
Are you saying triangle in nothing but a circle with three legs to stand on.....
 
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