#### Question

Find two nurnbers whose mean proportional is 12 and the third proportional is 324.

#### Solution

Let a and b be the two numbers, whose mean proportional is 12.

∴ ab =12^{2} ⇒ ab = 144 ⇒ b = `144/"a"` ...........(i)

Now, third proportional is 324

∴ a : b : : b : 324

⇒ `(144/"a")^2 = 324 "a"`

⇒ `(144)^2/"a"^2 = 324 "a"`

⇒ a^{3} = `(144 xx 144)/324`

⇒ a^{3} = 64

⇒ a = 4

b = `144/"a" = 144/4 = 36`

Therefore, numbers are 4 and 36

Is there an error in this question or solution?

Solution Find Two Nurn Bers Whose Mean Proportional is 12 and the Third Proportional is 324. Concept: Proportions.