Question

What is the circumference of a circle circumscribed around a rectangle with sides 7 cm and 24 cm?

Answer 1

The circumference of a circle is $\boxed{26\pi {\text{ cm or 81}}{\text{.70}}}.$

Further explanation:

Given:

The sides of the rectangle are 10 cm and 24 cm.

Explanation:

The Pythagorean formula can be expressed as,

$\boxed{{H^2} = {P^2} + {B^2}}$

Consider the radius of the circle as $r$.

The radius of the circle can be obtained as follows,

$\begin{aligned}{r^2} &= {5^2} + {12^2}\\{r^2} &= 25 + 144\\{r^2} &= 169\\r&= \sqrt {169}\\r&= 13\\\end{aligned}$

The formula for the circumference of the circle can be expressed as follows,

$\boxed{{\text{Circumference of circle}} = 2\pi r}$

The circumference of the circle can be obtained as follows,

$\begin{aligned}{\text{Circumference}} &= 2\pi r\\&= 2 \times \pi \times 13\\&= 26\pi\\&= 26 \times 3.14\\&= 81.70{\text{ cm}}\\\end{aligned}$

The circumference of a circle is $\boxed{26\pi {\text{ cm or 81}}{\text{.70}}}.$

Learn more:

1. Learn more about inverse of the function brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function brainly.com/question/3412497.

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: circle, rectangle, circumference, area, circumscribed, inscribed, length of circle, 10 cm, 24 cm, length of rectangle, radius, diameter.

Answer 2

Answer:

  25π cm ≈ 78.54 cm

Step-by-step explanation:

The diameter of the circumscribing circle is the diagonal of the rectangle.

You may recognize the rectangle dimensions as the numbers in the (7, 24, 25) Pythagorean triple. If not, you can compute the diagonal length from ...

  d = √(7²+24²) = √(49+576) = √625 = 25 . . . . centimeters

The circumference of the circle is π times the diameter:

  C = πd = 25π cm