Question

By using formula of mean proportional and third
proportional, find the ratio of third proportional to 8 and 20
and mean proportional between 4 and 9.
​

Answer 1

Step-by-step explanation:

Let the third proportion of 8 and 20 be x

$\frac{8}{20} = \frac{20}{x}$

$8x = 20 \times 20$

$8x = 400$

$x = \frac{400}{8}$

$x = 50$

Let the mean proportional of 4 and 9 be y

$\frac{4}{y} = \frac{y}{9}$

${y}^{2} = 4 \times 9$

${y}^{2} = 36$

$y = \sqrt{36}$

$y = 6$

The ratio of third proportional and mean proportional

= 50 : 6

= 25 : 3

Answer 2

Answer :

›»› The ratio of third proportional and mean proportional is 23 : 3.

Given :

• 8 and 20.
• 4 and 9.

To Find :

• The ratio of third proportional and mean proportional.

Solution :

Let us assume that, the third proportional of 8 and 20 is "x".

According to the first condition,

→ 8/20 = 20/x

By cross multiplication,

→ 8 * x = 20 * 20

→ 8x = 20 * 20

→ 8x = 400

→ x = 400/8

→ x = 100/2

→ x = 50

Again, let us assume that, the mean proportional of 4 and 9 is "y".

According to the second condition

→ 4/y = y/9

By cross multiplication,

→ 4 * 9 = y * y

→ 36 = y²

→ y² = 36

→ y = √36

→ y = 6

Now, the ratio of third proportional and mean proportional = third proportional of 8 and 20 : mean proportional of 4 and 9.

→ Ratio = 50 : 6

→ Ratio = 25 : 3

Hence, the ratio of third proportional and mean proportional is 23 : 3.