Question

I need to reask this:

I need help with this since my school switched teachers and we didnt take it and the new teacher is refusing to teach us it

Answer 1

let's pry open the triangles a bit and plug their values for the pythagorean theorem to get the hypotenuse, Check the picture below, those are only the first 4 triangles, notice the hypotenuse.

now let's move like the crab, backwards, let's do D first and then C

D)

well, since for the 1st triangle the root has a "2", that means "1+1", and it's pretty much the same for any subsequent triangle, so the rule must be

`{\Large \begin{array}{llll} P_(n)=√(n+1) \end{array}}\hspace{5em}\textit{rule for the }n^(th)~triangle`

C)

what does that make the 9th one?

`{\Large \begin{array}{llll} P_(9)=√(9+1)\implies P_9=√(10) \end{array}}`