Respuesta :
Answer:
The circumference of the circle = 26π unit.
Step-by-step explanation:
Given:
Radius of the circle, r = "x+6"
Diameter of the circle, d = "3(x)+5"
We have to find the circumference of the circle in terms of pi.
Formula to be used:
Circumference of a circle = 2πr or πd
As we know that:
Radius = Half of diameter
So,
⇒ [tex]radius=\frac{diameter}{2}[/tex]
⇒ [tex]x+6=\frac{3x+5}{2}[/tex]
⇒ [tex]2\times (x+6)=\frac{3x+5}{2}\times 2[/tex]
⇒ [tex]2x+12=3x+5[/tex]
⇒ [tex]12-5=3x-2x[/tex] ...Arranging variables and constants.
⇒ [tex]7=x[/tex]
Plugging x = 7 we will find the radius and the diameter.
⇒ Radius = "x+6" = "7+6" = 13
⇒ Diameter = "3(x)+5" = 3(7)+5 =26
Lets find the circumference of the circle.
⇒ Circumference = [tex]2\pi r= 2\pi (13) = 26 \pi[/tex] Or
⇒ Circumference = [tex]\pi d=\pi (26)=26\pi[/tex]
The circumference of the circle = 26π unit.
