Question

the areas of two circles are in the ratio 49:25
find the ratio of their circumference

Answer 1

Answer:

Step-by-step explanation:

Let the radius of circle 1 be R

and radius of smaller circle be r

Area of circle 1/Area of circle 2=49/25

πR^2

----------. =49/25

πr^2

Cancelling π

(R/r)^2=49/25

R/r=7/5

Perimeter of circle1/ perimeter of circle 2. =2πR/2πr

Cancelling 2 π

Perimeter of circle1/ perimeter of circle 2 = R/r = 7/5

Ratio of circumference =7:5

Best of luck.

Cheers !!!!!!!

Answer 2

Step-by-step explanation:

Let the radius of two semicircles be $r_1$ and $r_2$

→ Given :-

▶ The ratio of areas of two semicircles = 49:25 .

$\begin{lgathered}= > \frac{a_1}{a_2} = \frac{49}{25} . \\ \\ = > \frac{ \frac{ \cancel\pi {r_1}^{2} }{ \cancel2} }{ \frac{ \cancel\pi {r_1}^{2} }{ \cancel2} } = \frac{49}{25} . \\ \\ = > {( \frac{r_1}{r_2}) }^{2} = \frac{49}{25} . \\ \\ = > \frac{r_1}{r_2} = \sqrt{ \frac{49}{25} } . \\ \\ = > \frac{r_1}{r_2} = \frac{7}{5} .\end{lgathered}$

→ To find :- &&&&---

▶ The ratio of their circumference.

$\begin{lgathered}\therefore \frac{c_1}{c_2} \\ \\ = \frac{ \cancel\pi r_1}{ \cancel\pi r_2} . \\ \\ = \frac{r_1}{r_2} . \\ \\ = \boxed{ \green{ \frac{7}{5} .}}\end{lgathered}$

Hence, ratio of their circumference is 7 : 5 .