for Knights

posted by .

have been looking at your post ...

interesting question...

let the altitude of 12 hit base a
let the altitude of 14 hit base b

then (1/2)(12)a = (1/2)(14)b
6a = 7b
a = 7b/6

let the third side be c and its altitude be x

from the properties of the sides of a triangle
c < a+b
c < 7b/6 + b
c < 13b/6

but by area property
cx = 7b or cx = 6a

take cx = 7b
the absolute maximum value that c could be is a number just a "smidgeon" less than 13b/6 , which is positive , so divide both sides of
cx = 7b by that

cx/c < 7b / (13b/6)

c < 42/13

since you want the largest integer, that would be 3

( I am a little uneasy about my last division of the inequality)

  • for Knights -

    me too. You are dividing by c, which is less than 13b/6. The result will be larger than 42/13. What do you think of my attempt on the question as posted earlier?

  • for Knights -

    thanks a lot guys for your interest. Yes, it is somewhat of a confusing problem. @Steve: I appreciated it a lot and you did a very good job at explaining it.

    Thanks a lot guys and Happy New year. take care!

  • for Knights -

    In a right triangle, if the legs (altitudes are 12 and 14), then
    if we pick an angle θ and let h be the altitude to the hypotenuse,
    h/14 = sinθ
    h/12 = cosθ
    so h^2/144 + h^2/196 = 1, and h =~ 9.1

    So, Reiny's estimate is way low. Now the question is, does a right triangle provide maximum 3rd altitude h?

    More thought needed.

  • for Knights - Ta Daaaa -

    Take a look at

    where this very question is discussed.

  • for Knights -

    Just a final note. Since the 3rd altitude h is bounded by

    1/a + 1/b <= 1/h <= 1/a - 1/b
    where a < b,

    the limiting case where a=b (an isosceles triangle) shows that

    1/a+1/a <= 1/h <= 1/a - 1/a
    2/a <= 1/h <= 0
    shows that h >= a/2, and may grow without bound.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. English

    In modern English, the comparative/superlative for the word "bad" is indicated as worse/worst. A number of years ago, it was worse/worse. When did this change?
  2. social project

    the need to preserve and protect konark temple Answered before:
  3. if you're in the mood for riddles

    The riddle forum is back up: There are some truly clever riddles being posted. The following is one of my favorites. Try not to scroll down because then you'll see the answer(s):
  4. English

    anyone know where my other question went regarding the mythology sources?
  5. written communication

    What steps would one take to ensure that the purpose of your message (whether informative, negative, or persuasive) is conveyed to your readers?
  6. Algebra 2 - reposted for Erin
  7. Arts/social science

    What is the relevance of academic study of the Bible today,especially in African context?
  8. Spanish for Alicia and/or Vicky

    Be sure you see all 3 of your posts: 1.
  9. To Kuromi - re English and
  10. To Al 92 I haven't been on in a few days, but noticed you posted that follow up question. Sorry I missed it.

More Similar Questions