Question

what is the mean proportiional between 1.8 & 3.2 and third
proportional of 5 & 3?​

Answer 1

Step-by-step explanation:

Let the mean proportional between 1.8 and 3.2 be 'x'

1.8 : x : : x : 3.2

$\frac{1.8}{x} = \frac{x}{3.2}$

${x}^{2} = 5.76$

$x = \sqrt{5.76}$

$x = 2.4$

The mean proportion is 2.4.

Let the third proportional between 5 and 3 be 'x'.

5 : 3 : : 3 : x

$\frac{5}{3} = \frac{3}{x}$

$5x = 9$

$x = \frac{9}{5}$

The third proportion is 9/5.

Answer 2

Given,

Mean proportional 1.8 and 3.2 = (1.8 * 3.2) ^ (1/2) = 2.4

Third proportional of 5 and 3 = 9/5 = 1.8

Required Ratio =2.4/1.8 = 4/3