Explanation:
rect 1 with length and width as x and y
rect 2 with length and width as kx and ky
a) they are similar because kx/x = ky/y =k
sides are in a proportion,angles are obviously equal to 90°
b) perimeter of rect 1 = 2(x+y)
perimeter of rect 2 = 2(kx+ky)
(2k(x+y))/(2(x+y))= k
c) area of rect 1 = x*y
area of rect 2 = kx*ky = k^2*x*y
area 2/area 1 = k^2
hence the proof
wax question
volume of wax cube which are melted = 4^3= 64
volume of square pyramid = a^2 *(h/3)
a = area of base = 81
v = 81*10/3= 810/3= 270
no of wax cubes required = 270/64 = 4.24 cubes