56. dig deeper! two rectangular, adjacent rooms share a
wall. one-foot-by-one-foot tiles cover the floor of each room.
describe how the greatest possible length of the adjoining
wall is related to the total number of tiles in each room. draw
a diagram that represents one possibility.
pressions and factors

Consider two adjacent rectangular rooms having Length=L, and, Breadth = B

Now Suppose the wall which is in between two rooms has a height or length =H.

Breadth of wall = B [ if the wall doesn't exceed the breadth of room]

Considering two rooms to be identical,

Area of each room= L × B square unit

Area of each tile = 1×1=1 square unit

Number of tiles required= L B ÷ 1= LB tiles( product of length and breadth of room is number of tiles required)

Suppose if,LB= N

B= N/L  (1)

Area of wall(W) = B×H= B H square unit

B =W/H (2)

Equating (1) and (2)

⇒N/L = W/ H

⇒H =w-z/N

⇒H =WL/LH

⇒H = W/B

 ⇒  H =area of wall / Breadth of room and wall