The circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm is [tex]\boxed{26\pi {\text{ cm or 81}}{\text{.70}}}.[/tex]
Further explanation:
The Pythagorean formula can be expressed as,
[tex]\boxed{{H^2} = {P^2} + {B^2}}[/tex]
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 [tex]r[/tex].
The radius of the circle can be obtained as follows,
[tex]\begin{aligned}{r^2} &= {5^2} + {12^2}\\{r^2} &= 25 + 144\\{r^2} &= 169 \\r&= \sqrt {169}\\ r&= 13\\\end{aligned}[/tex]
The circumference of the circle can be obtained as follows,
[tex]\begin{aligned}{\text{Circumference}}&= 2\pi r\\&= 2 \times \pi \times 13\\&= 26\pi\\&= 26 \times 3.14\\&= 81.70{\text{ cm}}\ \end{aligned}[/tex]
The circumference of a circle circumscribed around a rectangle with sides 10 cm and 24 cm is [tex]\boxed{26\pi {\text{ cm or 81}}{\text{.70}}}[/tex].
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.
