Question

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

Answer 1

a :b = b:c b^2=ac=196 a=196/c 

a:c =c:112 c^2 = 112 a = 112 x 196/c 

c^3 = 112 x 196 c= 28 a = 7 b=14 

ans 7 and 28

Answer 2

Answer:

The two numbers are 14 and 56.

Step-by-step explanation:

Given: Mean proportion =28

Third proportion c = 224

Let a, b be the required numbers

√ab=28

Squaring on both sides

ab =  $28^{2}$

    = 784

a =784/b ……………..eqn 1

We know that ac $=b^{2}$

$\begin{array}{l}{\mathrm{c}=\mathrm{b}^{2} / \mathrm{a}} \\ {224=\mathrm{b}^{2} / \mathrm{a}}\end{array}$

Substitute for a,

$\begin{array}{l}{224=b^{2} /(784 / b)} \\ {224=b^{3} / 784} \\ {224(784)=b^{3}} \\ {b^{3}=175616}\end{array}$

b = 56

Substitute the value of b in eqn 1

a = 784/56

a = 14

Therefore the required two numbers are 14 and 56