Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

Mr.Math Group Title

\(\large \large \text{ Fun With Mr.Math #2}\) Determine the side lengths of a right triangle if they are integers and the product of the legs' lengths equals three times the perimeter.

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. asnaseer Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    |dw:1328658036624:dw| \[\begin{align} ab&=3(a+b+c)\tag{a}\\ &\qquad\text{rearranging (a) we get:}\\ 3c&=ab-3(a+b)\\ \therefore 9c^2&=a^2b^2-6ab(a+b)+9(a^2+b^2+2ab)\tag{b}\\ &\qquad\text{from Pythagorus we get:}\\ a^2+b^2&=c^2\\ \therefore 9a^2+9b^2&=9c^2\\ &=a^2b^2-6ab(a+b)+9(a^2+b^2+2ab)\hspace{2cm}\text{[using (b)]}\\ \therefore ab&=6(a+b-3)\tag{c}\\ &\qquad\text{substituting (c) into (a) we get:}\\ 6(a+b-3)&=3(a+b+c)\tag{d}\\ \therefore a+b-c&=6 \end{align}\] The solution is therefore al Pythagorean triples satisfying (d), which leads to these unique solutions: a=7, b=24, c=25 a=8, b=15, c=17 a=9, b=12, c=15 We can get 3 more solutions by swapping the values for a and b but I believe that these would not add anything new.

    • 2 years ago
  2. Mr.Math Group Title
    Best Response
    You've already chosen the best response.
    Medals 4

    Very good and neat asnaseer, as always! :-)

    • 2 years ago
    • Attachments:

See more questions >>>

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
  • 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.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.