QUESTION 8
Easy
The ratio of the perimeters of two circles is 5:4. What is the ratio of their radii?
SOLUTION
Given,
Ratio of perimeters of two circles is 5:4.
Since \(Circumference,\,C\, =\, 2πr\),
the constant 2π is the same for both circles.
Therefore,
\(\frac{C_1}{C_2}\,=\,\frac{r_1}{r_2}\)
So, \(\frac{r_1}{r_2} = \frac{5}{4}\)
The ratio of their radii is also 5:4.
Ratio of perimeters of two circles is 5:4.
Since \(Circumference,\,C\, =\, 2πr\),
the constant 2π is the same for both circles.
Therefore,
\(\frac{C_1}{C_2}\,=\,\frac{r_1}{r_2}\)
So, \(\frac{r_1}{r_2} = \frac{5}{4}\)
The ratio of their radii is also 5:4.
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Final Answer : The ratio of their radii is 5:4.
Concept Note
The circumference(perimeter) of a circle is directly proportional to its radius.