Question

find third proportional to 1.6 and 14.4​

Answer 1

$\huge\mathcal\colorbox{lavender}{{\color{b}{✿Yøur-Añswer♡}}}$

$\large\bf{\underline{\red{VERIFIED✔}}}$

Part 1:

Let the mean proportional between 14.4 and 3.6 = b

=> b² = 14.4 * 3.6

=> b² = 144*36/10*10

=> b = 12*6/10

=> b = 36/5

Part 2:

Let the third proportional of 5 and 4 = c

=> 4² = 5*c

=> c = 16/5

The required ratio is $\frac{\frac{36}{5} }{\frac{16}{5} }$

= 36/16

= 9/4

= 9:4

The ratio of the mean proportional between 14.4 and 3.6 and the third proportional of 5 and 4 is 9:4

Remember:

If a, b and c are in continued proportion,

a is the first proportional

b is the mean proportional

c is the third proportional

If a, b and c are in continued proportion, it is denoted as:

=> $\frac{a}{b} = \frac{b}{c}$

=> b² = ac

$\boxed{I \:Hope\: it's \:Helpful}$

${\sf{\bf{\blue{@ℐᴛz ᴅɪɴᴜ࿐}}}}$

Answer 2

Answer:

$\huge{\tt{\red{}\green{A}\purple{N}\pink{S}\blue{W}\orange{E}\red{R}}}$

Let the mean proportional between 14.4 and 3.6 = b

=> b² = 14.4 * 3.6

=> b² = 144*36/10*10

=> b = 12*6/10

=> b = 36/5

Let the third proportional of 5 and 4 = c

=> 4² = 5*c

=> c = 16/5

The required ratio is 516536

= 36/16

= 9/4

= 9:4

The ratio of the mean proportional between 14.4 and 3.6 and the third proportional of 5 and 4 is 9:4

Remember:

If a, b and c are in continued proportion,

a is the first proportional

b is the mean proportional

c is the third proportional

If a, b and c are in continued proportion, it is denoted as:

=> 

=> b² = ac