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
The circumference of a circle is [tex]\boxed{26\pi {\text{ cm or 81}}{\text{.70}}}.[/tex]
Further explanation:
Given:
The sides of the rectangle are 10 cm and 24 cm.
Explanation:
The Pythagorean formula can be expressed as,
[tex]\boxed{{H^2} = {P^2} + {B^2}}[/tex]
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 formula for the circumference of the circle can be expressed as follows,
[tex]\boxed{{\text{Circumference of circle}} = 2\pi r}[/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 is [tex]\boxed{26\pi {\text{ cm or 81}}{\text{.70}}}.[/tex]
Learn more:
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.
