The ratio of the perimeters of two circles is 5:4. What is the ratio of their radii?

Question

Homi · Accepted Answer

We will use the formula for the perimeter of a circle to find the ratio of their radii.

Step 1 — Define variables

Let's name the radius of the first circle R. Let's name the radius of the second circle r. We are given the ratio of their perimeters. This ratio is 5:4.

Step 2 — Use the perimeter formula

The perimeter of a circle is $2\pi$ times its radius. So, the perimeter of the first circle is $2\pi R$ . The perimeter of the second circle is $2\pi r$ . We can write the given ratio as an equation.

$\frac{\text{Perimeter of first circle}}{\text{Perimeter of second circle}} = \frac{5}{4}$

$\frac{2\pi R}{2\pi r} = \frac{5}{4}$

We can cancel out the common terms $2\pi$ .

$\frac{R}{r} = \frac{5}{4}$

This means the ratio of their radii is 5:4.

$\boxed{R : r = 5 : 4}$

Answer

The ratio of their radii is 5 : 4.

Question 8

Answer

More questions in Exercise 6.1