Question

prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.

Answer 1

let the sides of two similar triangles be (a, b, c) and (x, y, z).
such that a:x=b:y=c:z=k
therefore
a=kx,b=ky,c=kz
therefore the perimeters will be (kx+ky+kz)=k(x+y+z),(x+y+z)
the ratio of perimeters=k(x+y+z):x+y+z=k