Tile Problem Help Needed!

[Maron]

A problem from a highschool maths book.....

ive been trying to work this one out for years.

 

Mr and Mrs Wombat live in a house in which the floor of every room is a square and covered with identical square tiles. Mrs Wombat's room contains 101 tiles more than Mr Wombat's room. How many tiles does Mrs Wombat's room contain?

[Phi for All]

You've been trying for years? Since the rooms are square the tiles are even multiples, like 4x4, 5x5, 6x6, etc. There's probably a formula but you can just keep multiplying numbers by themselves to find the answer. Or find a multiplication table that goes up that high.

 

Her multiple is only one higher than his multiple, if that helps you with a starting point.

[Tartaglia]

Let small room be n*n and large (n+m)*(n+m)

 

ie (n+m)^2 -n^2 = 101

or m*(2n+m) = 101

 

ie m is a factor of 101, which is prime

therefore m = 1, n =50