Question

find the mean proportion of 18 and 72
please explain me ​

Answer 1

Step-by-step explanation:

Given :-

The numbers are 18 and 72

To find :-

Find the Mean Proportional ?

Solution :-

Method -1:-

Given numbers are 18 and 72

Let the Mean Proportional be X

=> 18 : X : : X : 72

Product of Means = X×X = X²

Product of Extremes = 18×72 = 1296

We know that

In proportion, Product of Means = Product of Extremes

=> X² = 1296

=> X = ± √1296

=> X = ±36

Since ,The given numbers are positive,

Therefore, X = 36

The Mean Proportional = 36

Short cut:-

Given numbers = 18 and 72

Let a = 18 and b = 72

We know that

The Mean Proportional of a and b is √(ab)

The Mean Proportional of 18 and 72

=> √(18×72)

=> √1296

=> 36

The Mean Proportional = 36

Answer :-

The Mean Proportional of the numbers 18 and 72 is 36

Used formulae:-

→ In proportion, Product of Means = Product of Extremes

→ The Mean Proportional of a and b is √(ab)