1. ## Write A Function

Marta gets paid only when she finishes tiling a room. the first rooms that Marta tiled were all square rooms. Write a function S such that S(n) expresses the number of tiles required to cover a square floor that has n tiles along the edge of the room. Include the domain of the function in your answer.

2. If there are n tiles along the entire edge of a square room, then let x be the number of tiles along one width of the room. Thus there must be x-2 tiles along one length of the room (We can't count a tile twice; draw a picture to help visualize this).

Thus we can obtain an expression for n:
$\displaystyle n = 2x+2(x-2) = 2(x+x-2)=4(x-1)$.

Solving for x in terms of n:
$\displaystyle x=\dfrac{n}{4}+1$.

Since x denotes the number of tiles along the width of the room, and the room is a square, the total number of tiles is $\displaystyle x^{2}$. Hence
$\displaystyle x^{2} = \left(\dfrac{n}{4}+1\right)^{2}$.

Therefore, $\displaystyle S(n) = \left(\dfrac{n}{4}+1\right)^{2}$.

Since the smallest square room possible for n tiles along the edge is n = 4 (a 2x2 tile room), then the domain of $\displaystyle S(n)$ is all $\displaystyle n \ge 4$.

3. ## ok....

Originally Posted by Pn0yS0ld13r
If there are n tiles along the entire edge of a square room, then let x be the number of tiles along one width of the room. Thus there must be x-2 tiles along one length of the room (We can't count a tile twice; draw a picture to help visualize this).

Thus we can obtain an expression for n:
$\displaystyle n = 2x+2(x-2) = 2(x+x-2)=4(x-1)$.

Solving for x in terms of n:
$\displaystyle x=\dfrac{n}{4}+1$.

Since x denotes the number of tiles along the width of the room, and the room is a square, the total number of tiles is $\displaystyle x^{2}$. Hence
$\displaystyle x^{2} = \left(\dfrac{n}{4}+1\right)^{2}$.

Therefore, $\displaystyle S(n) = \left(\dfrac{n}{4}+1\right)^{2}$.

Since the smallest square room possible for n tiles along the edge is n = 4 (a 2x2 tile room), then the domain of $\displaystyle S(n)$ is all $\displaystyle n \ge 4$.
Thank you. I would have never been able to come up with the correct function.

4. Originally Posted by deleted post
S(n) = the number of tiles required.
The room is square (and assuming the tiles are square):
n = length of room in tile lengths = width of room in tile lengths
So Area of floor = n x n = n^2
So S(n) = n^2
The minimum length of the room must be 1 tile length for it to be tillable, so domain: n>=1. Sorry for the edit.
This is my first answer I hope it's right and I hope it makes sense.
All the best.
You have misunderstood the question I think (although there is some ambiguity in the wording of the question). I think n is the total number of tiles around all sides of the room, not the number of tiles along one side. The correct answer is given in post #2.

5. ## Thanks...

I want to thank all who took time to help with this question.

Happy New Year!