### Extension of liethagoras theorem - By me

Liethagoras gave me a hint to discover this theorem or fact. He said that square of length of smallest side of a right triangle is equal to sum of lengths of other two sides. But I correct the statement. He had reached his victory but it has a small mistake. The correct statement which was given by me is "the square of smallest side in right triangle is equal to x(sum of lengths of other two sides).

If 'c' is hypotenuse and a>b.

then 'b' square = x(a+c).

I think this is 1st time to discover the above fact.

**Statement**:- In a right triangle smallest side square is divisible by sum of other two sides.

Given,

triangle ABC with right angle at C

By pathagoras theorem,

c Sq. = a sq. + b sq.

a sq = c sq - b sq

dividing both side by c+b we get,

a sq. = (c+b)(c-b)

let c-b = x

a sq. = x(c+b)

hence proved

here x is (c-b)

verification:-

let a=6,b=8,c=10

6 sq. is divisible by 8+10.

And other factor is (10-8)=2.

hence verified.

Check it out and Correct me if I am wrong.