+0

# Mensuration

+4
97
2
+72

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
Sort:

#1
+18246
+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
+74982
+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

### 10 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details