Question

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Answer 1

(a) The perimeter of the shape is the sum of half a circumference and the diameter itself.

The circumference of a circle with radius $r$ is $2\pi r$, and since $d=2r$ we can write the circumference as

$C=\pi d$

So, half a circumference is

$\dfrac{C}{2}=\dfrac{\pi d}{2}$

Ad we get the perimeter by addind the diameter:

$P=\dfrac{\pi d}{2}+d$

(b) Given the perimeter, we can solve for $d$:

$51.42=\dfrac{\pi d}{2}+d=d\left(\dfrac{\pi}{2}+1\right)$

So, we can divide both sides by the parenthesis and we have

$d=\dfrac{51.42}{\frac{\pi}{2}+1}=\dfrac{51.42}{2.571}=20$