geometry question...please help asap?

Question

find the length of the hypotenuse of the largest pythagorean triple triangle in which 16 is the measure of a leg. show the analysis tjat leads to your conclution..

what is a pythagorean triple..and how do you solve the problem?

Answer 1

you have to find 3 numbers for wich holds the equation :
a^2 + b^2 = c^2

solutions a,b,c are called pythagorean triplets

your teacher has given that a = 16. it is up to you now to find a b and c such that the minimum of a and b is as big as possible.

ther are tables for these triplets you can find them on the internet

see http://www.friesian.com/pythag.htm

the largest you can get with 16 is based on the 3,4,5 triplet

you can multioply eacht number with 4 and you get 12,16,20 <= the solution.

12^2 + 16^2 = 20^2

NB your teach has to define what is the largest triplet.( i just made a guess what she meant )

Answer 2

First, get a definition for "pythagorean triple":
http://en.wikipedia.org/wiki/Pythagorean_triple

"A Pythagorean triple consists of three positive integers a, b, and c, such that a^2 + b^2 = c^2."

Pythagorean triples can be generated by the following:

If m and n are two positive integers with m > n, then
a=m^2 - n^2
b= 2mn
c=m^2 + n^2

Answer 3

You are looking for integers with no common factor and p2+q2=r2.
So here you want r and q odd such that (r-q)(r+q)=256; So r-q=2 and r+q=128 gives you the largest possible r and q that is r= 65 and q=63. Happy?

Answer 4

Pythagorean Triplets

you were given leg a = 16

The formula to solve for b

b = (a/2)² - 1

b = (16/2)² - 1

b = (8)² - 1

b = 64 - 1

b = 63

- - - - - - - -

Solving for leg c

c = b + 2

c = 63 + 2

c = 65

- - - - - - - - s-

Answer 5

a^2+b^2=c^2
c-hypotenuse
the formular is only allowed when there`s a right angle in the triangle. c is the side opposite of the right angle.