Question

5. Find the mean proportional between 4 and 16.

6. Find the mean proportional between 5 and 45.

7. Find the mean proportional between 0.9 and 1.6.

8. Find the third proportional to 3 and 9.

9. Find the third proportional to 36 and 18.

10.Show that 10, 20 and 40 are in continued proportion.​

Answer 1

Answer:

5 : Mean proportional of 16 and 4 = √16×4

= √64

=8.

6 : Mean proportional of 5 and 45 = √5×45

= √ 225

= 15

7 : Mean proportional of 0.9 and 1.6 =√0.9×1.6

=√1.44

=1.2

9 : Let the required third proportional be x

∴ 36, 18, x are in continued proportion

⇒ 36 : 18 = 18 : x

⇒ 36x = 18 × 18

⇒ x = (18 × 18)/36

⇒ x = 9

10 : We know that if a,b and c are in continued proportion.

Then b*2 =ac.

Let a=10,b=20 and c=40

=> 20*2=10×40

=>200=200

Thus, given numbers are in continued proportion.