Question

In an isosceles triangle ABC right angled at B prove that AC^2=2AB^2

Answer 1

In isos. tri ABC, angle B =90
AB=BC(iso tri.)
By Pythagorus Theorem:-
AC^2=AB^2 + BC^2
AC^2=AB^2 + AB^2 (AB=BC, so AB^2 = BC^2 )
AC^2=2AB^2
Hence Proved!