Question

5 multiple choice 1 point a rope is laid on the ground in the shape of a circle of radius 27 inches. the same rope is then formed into the shape of a rectangle. if the width of the rectangle is 17 inches, find the length of the rectangle in inches. (round your answer to the nearest hundredth of an inch.) 68.21 67.82 67.25 67.57 67.94

Explanation:

Step1: Find the length of the rope (circumference of the circle)

The formula for the circumference of a circle is $C = 2\pi r$. Given $r = 27$ inches, then $C=2\pi\times27= 54\pi$ inches.

Step2: Set up an equation for the perimeter of the rectangle

The perimeter of a rectangle is $P = 2(l + w)$. The perimeter of the rectangle is equal to the length of the rope, so $P=54\pi$. We know $w = 17$ inches. Substituting into the perimeter formula gives $54\pi=2(l + 17)$.

Step3: Solve for the length $l$ of the rectangle

First, divide both sides of the equation $54\pi=2(l + 17)$ by 2: $27\pi=l + 17$. Then, subtract 17 from both sides: $l=27\pi- 17$.
Calculating $l=27\times3.14159 - 17=84.823 - 17=67.823\approx67.82$ inches.

Answer:

67.82