We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
+8
1979
2
avatar+132 

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.

 May 18, 2017
 #1
avatar+22290 
+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.

 

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

 

laugh

 May 18, 2017
 #2
avatar+101149 
+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) 

 

 

 

cool cool cool

 May 18, 2017

18 Online Users

avatar