Question

A square fl oor of the dimensions 72 cm 72 cm has to be laid with rectangular tiles whose length and breadth are in the ratio 3:2. What is the di erence between the maximum number of tiles and minimum numbers of tiles, given that the length and the breath are integers

Answer 1

Answer:

858  Tiles

Step-by-step explanation:

A square floor of the dimensions 72 cm 72 cm has to be laid with rectangular tiles whose length and breadth are in the ratio 3:2

Let say Length = 3A cm  then Breadth = 2A cm

Area of one Tile = 3A * 2A = 6A²   cm²

Area of Floor = 72 * 72 cm²

Let say Number of Tiles = N

then  N (6A²)  = 72 * 72

=> 6N  Should be a Square

Minimum vale of N for Which it can be  a square is N = 6

for N = 6

6 * 6 A² = 72 * 72

=> A² = 12 * 12

=> A = 12

Maximum Value of N When A²  is minimum => A² = 1

N 6 * 1² = 72 * 72

=> N = 864

Minimum number of tiles = 6

Maximum number of tiles = 864

difference between the maximum number of tiles and minimum numbers of tiles = 864 - 6  = 858