Question

find 2 numbers such that the mean proportion between them is 36 and the third proportional to them is 288

Answer 1

Let a, b be the required numbers .

Given, Mean proportional = 28

√ab = 28

ab = 28² = 784 .

a = 784/b

Also, Given Third proportional " c " = 224 .

We know that, ac = b²

So. c = b²/a

But we know that c = 224 .

224 = b²/a.

Substitute the value of " a "

224(784/b) = b²

b³ = 224(784) = 175616

b = 56 .

We know that,

ab = 784

56a = 784

a = 14 .

Therefore, Required numbers are 14 , 56 .

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