Question

let the thirds proportional to 4.2,0.7

Answer 1

Let the third proportional be x. The, 4.2 : 0.7 :: 0.7 : x, i.e.,

4.2 / 0.7 =0.7 / x

=> 6 = 0.7 / x

x = 0.7 / 6 = 0.1166667.

Thus, the third proportional to 4.2 and 0.7 is 0.1166667.

Answer 2

a/b = b/c
'c' is the third proportion
a*c = b*b
c = b*b/a
c= 0.7*0.7/4.2 =  0.7/6 =0.117(approx)