Question

Q3. Find the mean proportional between:
(1) 16 and 4
(2) 144 and 16
(3)3 and 27
Explain it.​

Answer 1

Step-by-step explanation:

1) Let the mean proportional between 16 and 4 be 'x'.

$\frac{16}{x} = \frac{x}{4}$

$x \times x = 16 \times 4$

${x}^{2} = 64$

$x = \sqrt{64}$

$x = 8$

2) Let the mean proportional between 144 and 16 be 'x'.

$\frac{144}{x} = \frac{x}{16}$

$x \times x = 16 \times 144$

${x}^{2} = 2304$

$x = \sqrt{2304}$

$x = 48$

3) Let the mean proportional between 3 and 27 be 'x'

$\frac{3}{x} = \frac{x}{27}$

$x \times x = 27 \times 3$

${x}^{2} = 81$

$x = \sqrt{81}$

$x = 9$