A square wall is covered with square tiles. There are 85 tiles altogether along the two diagonals. How many tiles are there on the whole wall.

Jeffreymars16
May 18, 2017

#1
**+3 **

**A square wall is covered with square tiles. **

**There are 85 tiles altogether along the two diagonals. **

**How many tiles are there on the whole wall.**

\(\left(\dfrac{85+1}{2}\right)^2 = 43^2=1849\)

heureka
May 18, 2017

#2
**+3 **

Let's use a more simple example to figure this out.....

Look at the pic below :

Note that we have a total of 13 points on both diagonals..........add 1 to this = 14 and divide by 2 = 7.....so...letting n = 7 we have a grid with n^2 = 7^2 = 49 points (tiles)

So...in your case....we have 85 tiles (points) on both diagonals......add 1 to this = 86 and divide by 2 = 43.....so, now.....letting n = 43 we have a grid with 43^2 = 1849 points (tiles)......which is exactly what heureka found.....!!!

Another way to see this is that we have :

(n - 2)^2 interior points and 2 [ n + (n - 2) ] "border" points

Letting n = 7 we get (7 - 2)^2 + 2 [ 7 + 5] = 25 + 24 = 49 points (tiles)

And with n = 43 we get (43 - 2)^2 + 2 [ 43 + 41 ] = 1849 points (tiles)

CPhill
May 18, 2017