Since the triangles are similar we can find the scale factor by the formula:

scale factor = the longest side for XYZ / longest side of ABC

scale factor = 60 / 24

if we denote the scale factor with 'k' we can write

k = 60 / 24 = 5/2

then the sides of the similar triangle XYZ will be

XY = k*AB = (5/2)*10 = 25

YZ = k*BC = (5/2)*20 = 50

ZX = k*AC = (5/2)*24 = 60

and the perimeter of XYZ = XY + YX + ZX = 25 + 50 + 60 = 135 units.

Another way to solve this problem is by using the theorem : If two similar triangles have a scale factor of a : b, then the ratio of their perimeters is a : b.

Perimeter XYZ = scale factor * Perimeter ABC

Perimeter XYZ = (5/2) * (10 + 20 + 24) = 135 units.

The perimeter of XYZ is 135 units.