Question

The mean proportional between two numbers is 28 and their third proportional to them is 224. The two numbers are

Answer 1

Let a , b are the numbers.

since mean root is 28,

√(ab) = 28.


so, ab= 784

==> a = 784/b --(1)

Third propotion is 224

so , a, b , 224 are in propotion.

therefore, (a/b) = (b/224)

cross multiplying,

so , a× 224 = b^2 -->(2)

substitute (2) in (1)

(784/b)× 224 =b^2

therefore, (784×224) = b^3

therefore,b^3 = 175616

factorising,we get b= 56.

now substitute value of b in (1) to get a

a= 784/56 = 14.

sothe numbers are 14 & 56