Question

an athletic track is made of a rectangle and two semicircles as seen below where $x$ is the side length of the rectangular part and $r$ is the radius of the semicircles. determine the formula for the perimeter $p$ in terms of $x$ and $r$. $p =$ solve the perimeter formula for $x$. $x=$

Explanation:

Step1: Analyze the perimeter components

The two semi - circles together form a full circle with circumference $C = 2\pi r$, and there are two lengths of the rectangle each of length $x$. So the perimeter formula is $P=2x + 2\pi r$.

Step2: Solve for $x$

First, subtract $2\pi r$ from both sides of the equation $P = 2x+2\pi r$: $P - 2\pi r=2x$. Then divide both sides by 2: $x=\frac{P - 2\pi r}{2}$.

Answer:

$P = 2x+2\pi r$
$x=\frac{P - 2\pi r}{2}$