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# Find Two Nurn Bers Whose Mean Proportional is 12 and the Third Proportional is 324. - ICSE Class 10 - Mathematics

#### 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 =122 ⇒  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"

⇒ a3 = (144 xx 144)/324

⇒ a3 = 64

⇒ a = 4

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

Therefore, numbers are 4 and 36

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#### APPEARS IN

Frank Solution for Frank Class 10 Mathematics Part 2 (2016 to Current)
Chapter 9: Ratio and Proportion
Exercise 9.2 | Q: 14

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