Sunday, December 9, 2012

Q2/123) Find integer sided isosceles triangle whose area is integer



We have Pythagorean triplet that is integer length sides for a right angled triangle with hypotenuse c as
a= u^2-v^2
b= 2uv
and c = (u^2+v^2)

Now it may be noted that as b is even so ab/2 is integer.

Now if we double any of the base and hypotenuse as the two other sides we have area is integer

So the 3 sides are (u^2+v^2, u^2+v^2, 4uv) or (u^2+v^2, u^2+v^2, 2u^2-2v^2)

No comments: