Chapter 1.5, Problem 37E

(a).

To determine

To Find: To write a formula for the perimeter of the indoor track.

Answer to Problem 37E

The perimeter of indoor track is, $C=2x+2\pi r$

Explanation of Solution

Given Information: An indoor track is build up and shown in the figure.

Formula used: The formula for the perimeter is given by

  $\begin{array}{l}perimeter=2x+2\pi r\\ C=2x+2\pi r\end{array}$

Where C = perimeter

(b).

To Find: The formula for $x$ which is the length of rectangular portion as shown in the figure.

The formula for the $x$ is given by $x=\frac{C-2\pi r}{2}$

Given Information: An indoor track is build up and shown in the figure

Formula Used: The perimeter of the indoor track C is given by

  $\begin{array}{l}C=2x+2\pi r\\ C-2\pi r=2x\\ x=\frac{C-2\pi r}{2}\end{array}$

Hence, the formula for the $x$ is given by $x=\frac{C-2\pi r}{2}$

(c).

To Find: The value of the $x$ to the nearest foot.

The value of $x$ is 173 foot.

Given Information: The perimeter of the track is $660$ feet and the radius of semicircular portion is $r=50$ feet.

Formula used: $x=\frac{C-2\pi r}{2}$

Calculation:

  $\begin{array}{l}x=\frac{C-2\pi r}{2}\\ x=\frac{660-2\times 3.14\times 50}{2}\\ x=\frac{660-314}{2}\\ x=\frac{346}{2}\\ x=173feet\end{array}$

Hence,The value of the $x$ to the nearest foot.

(b).

To determine

To Find: The formula for $x$ which is the length of rectangular portion as shown in the figure.

Answer to Problem 37E

The formula for the $x$ is given by $x=\frac{C-2\pi r}{2}$

Explanation of Solution

Given Information: An indoor track is build up and shown in the figure

Formula Used: The perimeter of the indoor track C is given by

  $\begin{array}{l}C=2x+2\pi r\\ C-2\pi r=2x\\ x=\frac{C-2\pi r}{2}\end{array}$

Hence, the formula for the $x$ is given by $x=\frac{C-2\pi r}{2}$