Square wall covered in tiles

M

MathsFormula

Junior Member
Joined
Jul 13, 2014
Messages
95
A square wall is covered in square tiles. There are 85 tiles altogether along the two diagonals. How many tiles are there on the whole wall?

Book answer is 1849

My attempt below gave the WRONG ANSWER. Please advise:

Along one diagonal there must be 85÷2 tiles = 42.5 tiles

Let the length of the square wall be W

So using Pythagoras W2 + W2 = 42.52

(Square root of 2)*W = 42.5

W = 30.14

So number of tiles on whole wall = 30.14*30.14 = 908 WRONG ANSWER
 
MathsFormula said:
A square wall is covered in square tiles. There are 85 tiles altogether along the two diagonals. How many tiles are there on the whole wall?

Book answer is 1849

My attempt below gave the WRONG ANSWER. Please advise:

Along one diagonal there must be 85÷2 tiles = 42.5 tiles

Let the length of the square wall be W

So using Pythagoras W2 + W2 = 42.52

(Square root of 2)*W = 42.5

W = 30.14

So number of tiles on whole wall = 30.14*30.14 = 908 WRONG ANSWER
Click to expand...

Take a piece of graph paper and start counting.

If you have a 5 x 5 square - how many squares are on the two diagonals → 5 + 4

If you have a 7 x 7 square - how many squares are on the two diagonals → 7 + 6

If you have a 9 x 9 square - how many squares are on the two diagonals → 9 + 8

Now you have (43 + 42) squares on the diagonals → what is the size of the square?
 
Subhotosh Khan said:
Take a piece of graph paper and start counting.

If you have a 5 x 5 square - how many squares are on the two diagonals → 5 + 4

If you have a 7 x 7 square - how many squares are on the two diagonals → 7 + 6

If you have a 9 x 9 square - how many squares are on the two diagonals → 9 + 8

Now you have (43 + 42) squares on the diagonals → what is the size of the square?
Click to expand...

43 * 43 = 1849

First of all that was GENIUS getting me to draw a graph and work out tile numbers. Perfect solution. Thank you

Second. It is ridiculous that I should be required to think like this for geometry exams because drawing on a graph paper and counting tiles one by one seems so primitive.

I don't think I'm meant to just "know" to do this. Don't mathematicians just go straight to calculations and formulae?
What do you think S K?

I was expecting a mathematics formula with algebra and Pythagoras etc. Perhaps with a MINUS ONE to take into account the centre tile that had been counted twice.
 
Last edited:
Denis said:
Keep in mind that if n is odd, then there is a tile
(at center) that is "along" both diagonals.

n = number of tiles along the two diagonals (85)
t = total tiles (?)

General case formula:
if n is odd: t = [(n + 1) / 2]^2 ....... (86/2)^2 = 43^3 =1849
if n is even: t = (n / 2)^2

Can be one equation if FLOOR function used,
but I don't want to mix you up with that...
Click to expand...

To the corner .... for 3 minutes ...... right now.... and count to 300...
 
Denis said:
Keep in mind that if n is odd, then there is a tile
(at center) that is "along" both diagonals.

n = number of tiles along the two diagonals (85)
t = total tiles (?)

General case formula:
if n is odd: t = [(n + 1) / 2]^2 ....... (86/2)^2 = 43^3 =1849
if n is even: t = (n / 2)^2

Can be one equation if FLOOR function used,
but I don't want to mix you up with that...
Click to expand...

This is just depressing. From counting tiles to the Denis formula (that I don't know how he calculated) are two extremes. So must be something in the middle that is more basic?
 
Denis said:
Sumtin' "in the middle"? Well, this is not a culassroom so I don't
have blackboard and chalk to demonstrate.
Anyway, even if I did, I'd need to draw a couple of diagrams
and YES, count a few squares/tiles to demonstrate...which is
something apparently beneath your dignity...
Click to expand...

Counting squares is NOT beneath my dignity. I followed instructions given by Subhotosh and it helped. I am grateful.

Denis I wish you would be kind enough to show me in a few steps how you derived your formula. That would be the SOMETHIN' in the middle that I'm looking for.
 
Just wanted to say that I did not mean to appear ungrateful when I said that I was expecting a solution to the problem with formulae rather than number counting. Words / sentences that are written sometimes be misinterpreted.
Number counting solution from Subhotosh was an excellent idea that I was incapable of figuring out alone. Was very helpful and has provided me an idea that I can use for similar problems in the future.

The forum is great and has helped me so much in the short space of time I've been a member. Thanks to all.
 
Last edited:
Thanks Denis, I followed your thinking step by step and got to the solution.
So I have learnt slightly different ways of tackling this problem from yourself and Subhotosh ... different ways of thinking. Both very helpful.


Denis said:
Now you should be able to get a job as a tile installer:rolleyes:
Click to expand...

May I add Sir, that your wit is razor sharp :wink:
 
You must log in or register to reply here.
Top