Question

the area of two semicirles are in the ratio 49:25. find the ratio of their circumferences

Answer 1

area of first semicircle= pi(r1)square


area of second semicircle=pi(r2)square
ratio of areas =
pi(r1)square :pi(r2)square =49:25

r1:r2= 7:5
circumference of 1 semicircle = pi x 7
circumference of 2 semicircle = pi x 5
ratio of circumferences = pi x 7 : pi x 5=7:5

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 .