Solving Problems Without Guess & Check

[Ilikebugs]

Can we do this without guess and check? View attachment 6248

 

[topsquark]

I guess that depends, since we aren't given the radius...

-Dan

Edit: I guess the radius was mentioned. (Ahem!) (Angry)

 

[MarkFL]

The perimeter $P$ of the given sector is:

\(\displaystyle P=2n+n\frac{360}{n}\cdot\frac{\pi}{180}=2(n+\pi)\)

So, we want:

\(\displaystyle 20<P<30\)

\(\displaystyle 20<2(n+\pi)<30\)

\(\displaystyle 10<n+\pi<15\)

Can you continue

 

[Ilikebugs]

N can equal 7,8,9,10, or 11?

 

[MarkFL]

N can equal 7,8,9,10, or 11?

Well, let's see:

\(\displaystyle 10<n+\pi<15\)

\(\displaystyle 10-\pi<n<15-\pi\)

Let's use $\pi\approx3.14$:

\(\displaystyle 6.86<n<11.86\)

Hence:

\(\displaystyle n\in\{7,8,9,10,11\}\quad\checkmark\)