Question

Find two numbers whose mean proportional is 18 and the third proportional is 486. 

Answer 1

Let a and b be the two numbers, whose mean proportional is 18.

`therefore "ab" = 18<sup>2</sup> => "ab" = 324 => "b" = 324/"a"` ......(i)

Now, third proportional is 486 

∴ a : b : : b : 486

⇒ b² = 486 a

⇒ `(324/"a")^2` = 486  a

⇒ `(324)^2/"a"^2` = 486 a 

⇒ `"a"^3 = (324 xx 324)/486`

⇒ a³ = 216

⇒ a = 6

b = `324/"a" = 324/6 = 54`

Therefore, numbers are 6 and 54 .