word problems and turning them into algebraic equation to slove

Question

 The Tile company tiles rectangle areas. Ted lays the center tiles. Mary comes along and borders the area with gray tiles. ( For example, in a 1x3 area, Ted would lay the three center tiles and Mary would lay the 12 border tiles.)

Picture in this example a rectangle that is 3  square tiles by 5 square tiles in the border are gray , and  the 3 square tiles in the middle are white.

Suppose each tile is one square meter( unite area)

 

How many boarder tiles are needed for a 4x8 area( to be bordered)?

A 28X56 area ( to be bordered)?

A X x Y area ( to be bordered)?

Answer 1

Another pattern would be 2*L+2*W+4(one for each of the four corners to complete the border).

Answer 2

Use pattern to help you.

1x3 needs (1+2)(3+2)-1*3 = 12 boarder tiles

So, 4x8 needs (4+2)(8+2) - 4*8 = 28 boarder tiles.

 

In general,

XxY needs (X+2)(Y+2) - X*Y boarder tiles.