If the areas of three adjacent faces of a rectangular box which meet in a corner are $$ 12 cm^2,   15 cm^2    and   20 cm^2$$  respectively. Then the volume of the box is

let length , breadth , height be l, b, h respectively

$$l \times b $$ = 12 ------------- eq 1

$$b \times h $$ = 15---------------eq2

$$h \times l $$ = 20----------------eq3

multiply eq 1 by eq2  and dividing eq3

we get 

$$\frac{l \times b \times b \times h}{h \times l}$$  = $$b^2$$ = $$\frac{12 \times 15}{20}$$ 

b = 3

from eq 1 we get l = 4 

from eq 2 we get h = 5

volume of the cuboid = $$l \times b \times h$$ = $$3 \times 4 \times 5$$ =$$ 60  cm^3 $$