A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
All Pythagorean triples where area = perimeter (numerically)?
anonymous
 4 years ago
All Pythagorean triples where area = perimeter (numerically)?

This Question is Closed

RadEn
 4 years ago
Best ResponseYou've already chosen the best response.15,12,13 using trial and error method ^^

RadEn
 4 years ago
Best ResponseYou've already chosen the best response.1ok, general form tripel pythagorean number is : a=x b=(x^21)/2 c=(x^2+1)/2 with a<b<c (a,b,c are sides of a righttriangle) perimeter = area x + (x^21)/2 + (x^2+1)/2 = x(x^21)/2, simplify it we get : x^3  4x^2  5x =0 x(x^2  4x  5) = 0 x(x5)(x+1)=0 x=5 satifisfy it (so, a=5, b=12, c=13) with same way, for a=2x b=x^21 c=x^2+1 perimeter = area 2x+x^21+x^2+1 = 2x(x^21)/2, simplify it we get : x^3  2x^2  3x = 0 x(x^2  2x  3) =0 x(x3)(x+1)=0 x=3 satifisfy it (so, a=6, b=8, c=10) i have done for a=kx b=k(x^21) c=k(x^2+1) with k=3,4,5,6... there are x satisfy it but the result just reflication of on... and its rest not satisfy for x which make for a,b,c integer number

RadEn
 4 years ago
Best ResponseYou've already chosen the best response.1so, just 2 triple only...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.03,4,5 is a triple, too!

RadEn
 4 years ago
Best ResponseYou've already chosen the best response.1but, its area not equal its perimeter...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0you can have an easier algebra by eliminating z from x^2+y^2=z^2 and xy/2 = x + y +z leads to xy 4x 4y +8 = 0 > (x4)(y4) = 8 etc.

RadEn
 4 years ago
Best ResponseYou've already chosen the best response.1just combine of (x4)(y4) = 8, and we will get 2 triple only are : (x,y,z) = 5,12,13 and 6,8,10 but yours easier than me :)
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.