Question

The areas of two circles are in ratio 25:36.Find the ratio of their circumference.

pls give answer with explanation!

Answer 1

Ratio of areas of circles =25:36
=25/36
Radius of first circle = πr^2
Radius of second circle = πR^2
πr^2/πR^2 = 25/36
r^2/R^2 = 25/36
(r/R)^2 = 25/36
r/R = √25/36
r/R =5/6
Ratio of circumferences=2πr/2πR
=r/R
=5/6
Therefore, ratio of circumferences = 5:6 Ans

Answer 2

Hola !!!!

Let the areas be 36x and 25x

Let the radius of two circles be 'R' and 'r'

Therefore, Their area is .....

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Area of Circle with 'r' as radius = πr² = 25x

$r = \sqrt{ \frac{25x}{\pi} } = \frac{5 \sqrt{x} }{ \sqrt{\pi} }$


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Area of Circle with 'R' as radius = πR² = 36x

$R = \sqrt{ \frac{36x}{\pi} } = \frac{6 \sqrt{x} }{ \sqrt{\pi} }$


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Now, Circumference is ......

Circumference of circle with radius 'r' = 2πr

Circumference of circle with radius 'R' = 2πR

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Their ratio......

$\frac{2\pi \: r}{2\pi \: R} \\ \\ = \frac{r}{R} \\ \\ substituting \: values \: of \: r \: and \: R \: \\ \\ = \frac{ \frac{5 \sqrt{x} }{ \sqrt{\pi} } }{ \frac{6 \sqrt{x} }{ \sqrt{\pi} } } \\ \\ by \: taking \: reciprocal..... \\ \\ = \frac{5 \sqrt{x} }{ \sqrt{\pi} } \times \frac{ \sqrt{\pi} }{6 \sqrt{x} } \\ \\ = \frac{5}{6} \\ \\ so \: the \: ratio \: is \: 5: 6$


Hope it helps