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# Mensuration

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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
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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.

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

May 18, 2017
#2
+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)

May 18, 2017