Question

What is the circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm?

Answer 1

Answer:

81.7 cm

Step-by-step explanation:

Best that you draw both circle and rectangle.  The center of the rectangle coincides with the center of the circle.  From this center draw a vertical line segment to the upper edge of the rectangle.  Similarly, draw a horiz. line to the right edge.  The length of this vertical line segment will be half of 10 cm, or 5 cm; the length of this horiz. line segment will be half of 24 cm, or 12 cm.

Draw a diagonal from the center to the far corner (vertex) of the rectangle.  Using the Pythagorean Theorem, we determine that the length of this diagonal is d = √(5^2 + 12^2) = 13.  This is also the radius of the circle.

The circumference of the circle is thus C = 2πr, or C = 2π(13 cm), or

26π cm, or roughly 81.7 cm

Answer 2

The circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm is $\boxed{26\pi {\text{ cm or 81}}{\text{.70}}}.$

Further explanation:

The Pythagorean formula can be expressed as,

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

Here, H represents the hypotenuse, P represents the perpendicular and B represents the base.

Given:

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

Explanation:

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 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 circumscribed around a rectangle with sides 10 cm and 24 cm is $\boxed{26\pi {\text{ cm or 81}}{\text{.70}}}$.

Learn more:

Learn more about inverse of the function https://brainly.com/question/1632445.

Learn more about equation of circle brainly.com/question/1506955.

Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Circle

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