Question

Find two numbers such that the mean proportional between them is 12 and the third proportional to them is 96.​

Answer 1

Answer:

The numbers are 6 and 24.

Step-by-step explanation:

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

∴ ab = $12^2$  ⇒ ab = 144 ⇒ b = $\frac{144}{a} .........(1)$

Now, the third proportional is 96.

∴ a:b::b:96

$b^2 = 96a\\\\(\frac{144}{a})^2= 96a\\\\\frac{(144)^2}{a^2} = 96a\\\\a^3 = \frac{144*144}{96} \\\\a^3= 216\\\\a = 6\\\\b = \frac{144}{6} = 24$

Therefore, the numbers are 6 and 24.