Question

what is the mean proportion of 4 and 25?​

Answer 1

Answer:—

The mean proportional of 4 and 25 is 10.

Explanation:—

We have to find b such that 4 : b = b : 25. Thus we must have 4/b = b/25 .

Therefore b² = 4 × 25 = 100, which gives b = √100 = 10. (We can also take b = −10, since 4 : −10 = −10 : 25)

If three numbers a,b,c are such that a:b=b:c, we say c is the third proportion.

Answer 2

Step-by-step explanation:

The mean proportional of 4 and 25 is 10.

Let us consider b as the mean proportional between a and c [b is the mean proportional which we have to find]

We know a=4 and c=25

So we have

${b}^{2} = ac$

Substitute the value of a and c in the above eqn

Therefore,

${b}^{2} = 4 \times 25$

${b}^{2} = 100$

$b = \sqrt{100}$

$b = \frac{ + }{ - } 10$

Here b cannot be negative

Hence the value of b =10

Therefore mean proportional b=10