Question

find two numbers such that the mean proportional between them is 28 and the third
proportional to them is 224.​

Answer 1

≡QUESTION≡

Find two numbers such that the mean proportional between them is 28 and the third  proportional to them is 224.​

                                                                                 

║⊕ANSWER⊕║

Let a, b be the required numbers .

GIVEN

Mean proportional = 28

Third number proportional (c) = 224

√ab = 28

ab = 28² = 784 .

a = 784/b

We know that, ac = b²

So. c = b²/a

c = 224 .

224 = b²/a.

Substitute the value of " a "

224(784/b) = b²

b³ = 224(784) = 175616

b = 56

ab = 784 (Refer above)

56 a = 784

a = 14

∴ Required numbers are 14 and 56 .