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ttokoro
21-Topaz I
ttokoro21-Topaz I
21-Topaz I
May 15, 2025
Solved

Find the area ABD.

  • May 15, 2025
  • 3 replies
  • 1234 views

∠BAE=∠EAC, area BDE=1. Find area ABE.

 

image.png

Best answer by Werner_E

 

Werner_E_1-1747321498420.png

???? How could the triangle BDE have an area as much as 1 cm^2 ????

The max area possible is 0.45 cm^2 for theta=45°

Werner_E_2-1747321664479.png

ani25.gif

 

BTW, you know that the youtube link you posted is a picture and so is not clickable or text-copyable!? Sure you don't expect us to retype it. 😉

 

And then - the area of which triangle you really are looking for? The thread topic and in the Prime screenshot we read ABD, but the thread body and the screenshot header says ABE !??

 

3 replies

ttokoro
21-Topaz I
ttokoro21-Topaz IAuthor
21-Topaz I
May 15, 2025

Puzzle 24 is find integer a, b and c, But it is too hard to solve.

image.png

 

Puzzle 25 If you find a answer, how area size of BDE, that has the largest value, and find the area ABE.

t.t.
W
Werner_E25-Diamond I
25-Diamond I
May 15, 2025
@ttokoro wrote:

Puzzle 24 is find integer a, b and c, But it is too hard to solve.

 

Hmm, Mathcad is not made for calculations in number theory and so can't solve diophantic equations.

But using brute force it easily can find solutions like 4; -1; 11 or 9;-5;11 or a bit larger -81; -72; 40

Werner_E_4-1747322637775.png

 

    ttokoro
    21-Topaz I
    ttokoro21-Topaz IAuthor
    21-Topaz I
    May 16, 2025

    And also all positive integers a, b and c are available.

     

    a=154476802108746166441951315019919837485664325669565431700026634898253202035277999,
    b=36875131794129999827197811565225474825492979968971970996283137471637224634055579,
    c=4373612677928697257861252602371390152816537558161613618621437993378423467772036

     

    t.t.
    W
    Werner_E25-Diamond IAnswer
    25-Diamond I
    May 15, 2025

     

    Werner_E_1-1747321498420.png

    ???? How could the triangle BDE have an area as much as 1 cm^2 ????

    The max area possible is 0.45 cm^2 for theta=45°

    Werner_E_2-1747321664479.png

    ani25.gif

     

    BTW, you know that the youtube link you posted is a picture and so is not clickable or text-copyable!? Sure you don't expect us to retype it. 😉

     

    And then - the area of which triangle you really are looking for? The thread topic and in the Prime screenshot we read ABD, but the thread body and the screenshot header says ABE !??

     

      ttokoro
      21-Topaz I
      ttokoro21-Topaz IAuthor
      21-Topaz I
      May 16, 2025

      The original question is find the ratio S(BDE):S(AEC).

      t.t.
      W
      Werner_E25-Diamond I
      25-Diamond I
      May 16, 2025
      @ttokoro wrote:

      The original question is find the ratio S(BDE):S(AEC).

      3:8, independent from theta

       

      BDE : AEC : ABE : ABD : ABC = 3 : 8 : 12 : 15 : 20

       

      Werner_E_1-1747501025860.png

       

       

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