Question

if the sides of areas of two circle is1:16 ,then ratio in their perimeters is​

Answer 1

Answer:

Let the radii of the circles be r

1

​

& r

2

​

respectively.

Then, their circumferences are 2πr

1

​

& 2πr

2

​

, respectively.

So, their ratio=2πr

1

​

:2πr

2

​

=r

1

​

:r

2

​

.

Again, the areas of the circles are π(r

1

​

)

2

& π(r

2

​

)

2

.

Then, their ratio =π(r

1

​

)

2

:π(r

2

​

)

2

=(r

1

​

)

2

:(r

2

​

)

2

=16:25 ...(given).

∴(r

1

​

):(r

2

​

)=

16:25

​

=±(4:5)

We reject the negative value of r's since the radius is a length.

∴(r

1

​

):(r

2

​

)=(4:5).

Step-by-step explanation:

Answer 2

Answer:

Let the radii of the circles be r1 & r2 respectively.

Then, their circumferences are 2πr1 & 2πr2, respectively.

So, their ratio=2πr1:2πr2=r1:r2.

Again, the areas of the circles are π(r1)2 & π(r2)2.

Then, their ratio =π(r1)2:π(r2)2=(r1)2:(r2)2=16:25  (given).

∴(r1):(r2)=16:25=±(4:5)

We reject the negative value of r's since the radius is a length.

∴(r1):(r2)=(4:5).