Respuesta :
Answer:
[tex]2r(\sqrt{3}+1)[/tex]
Step-by-step explanation:
A rectangle is inscribed in a circle of radius r.
Radius of the circle is 'r' . the diameter of circle is 2 times radius is 2r
The diameter of the circle becomes the diagonal of the rectangle.
The one part of the rectangle forms a triangle with hypotenuse 2r
Triangle is a special 30:60:90 degree angle
the ratio of the special triangle is [tex]1: \sqrt{3} :2[/tex]
Hypotenuse is '2r' , so the ratio becomes
[tex]r: \sqrt{3}r :2r[/tex]
So the width of the rectangle is 'r' and length of the rectangle is [tex]\sqrt{3}r[/tex]
Perimeter = 2 times length + 2 times width
[tex]perimeter = 2\sqrt{3} r+2r=2r(\sqrt{3}+1)[/tex]
