R:- hypotenuse is given?

Question

I can find out the pythagorean triplets of a rt. triangle when opposite side or base is given.Can u find out the pythagorean triplets when hypotenuse of a rt. triangle is given?

Answer 1

Let there be a right-angled triangle.
now,
we know that,
(2n^2+2n+1)^2=4n^4 + 4n^2 + 1 + 2(4n^3 + 2n+ 2n^2)
=>(2n^2+2n+1)^2=4n^4 + 4n^2 + 1 + 8n^3 + 4n+ 4n^2
=>(2n^2+2n+1)^2=(4n^4 + 4n^2 + 8n^3) + (1 + 4n+ 4n^2)
=>(2n^2+2n+1)^2=(2n^2 + 2n)^2 + (2n+1)^2
This gives solutions
(3,4,5); (5,12,13); (7,24,25); (9,40,41)........................
the above relation is true for all n belonging to natural numbers
this way you can find solution for any pair of sides the 3rd side been given.
put the given side equal to one in equation and find positive n by solving the quadratic and find all the sides.
Eg:If hyputenuse is given as 5
Solve 2n^2 + 2n + 1= 5
=>n=1 therefore other sides are 3 and 4

Choose this as best, if correct.

Answer 2

There are tables of Pythagorean triplets. You can match up your hypoteneus with the corresponding triplet.

See the source below for a list of the triplets up to a hypoteneus length of 100.

Answer 3

with a right triangle, you can not find the lengths of the sides just by knowing the hypotenuse. you would need to know an angle (other than the 90)

Answer 4

You can not solve a triangle with 2 pieces of information.

Answer 5

Hello Rajesh
Do you mean primitive triplets or just any triplet ?
For primitive triplets you can find unique solution.

Here is the formula for your triplets
(a,b,c)=(2m,m^2-1,m^2+1).

Are you tiling your kitchen floor ;)

Answer 6

you need to know the one more side. however, if you are talking about an isoscles right triangle, you can figure out the other two sides.

Answer 7

you can find it out if you can construct the triangle with mathematical conscience a pencil a passer and a lineal.