Question

Two rectangular adjacent rooms share a wall 1‘ x 1‘ 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

Answer 1

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 =
`(WL)/(N)`

⇒H =
`(WL)/(LB)`

⇒H = W/B

⇒ H =
`\frac {\text{ Area of Wall}}{\text{Breadth of room or wall}}`