Answer:
17.2 cm
Step-by-step explanation:
If the same rope that is used to wrap a rectangular object is used to form a circle, then the perimeter of the rectangle is equal to the circumference of the circle.
The perimeter of a rectangle is twice the sum of its width and length, and the circumference of a circle with radius r is 2πr. Therefore:
[tex]\textsf{Perimeter}=\textsf{Circumference}\\\\2(24+30)=2\pi r[/tex]
To solve the equation for r, begin by dividing both sides of the equation by 2:
[tex]24+30=\pi r\\\\\\54=\pi r[/tex]
Now, divide both sides by π to isolate r:
[tex]r=\dfrac{54}{\pi}\\\\\\r=17.1887338539...\\\\\\r=17.2\; \sf cm\;(nearest\;tenth)[/tex]
Therefore, the radius of the circle rounded to the nearest tenth is:
[tex]\Large\boxed{\boxed{17.2\; \sf cm}}[/tex]
