Question

Rani, Geetha, and Naseema live near each other. The distance from their house to the road is 90 feet. They decided to tile the path to the road. They all bought tiles of different designs and lengths. Rani the shortest tile, Geetha bought the one and Naseema bought the longest one. If they could tile the path without cutting any of the tiles what is the size of the tiles each has bought? Suggest 3 different solutions. Explain how you get this answer.

Answer 1

Length of the path = 90 feet

For the tiles to be tiled on the path without cutting, the size of each tile should be a factor of 90.

Now 90 can be factorized as follows:

90 = 1 x 90

90 = 2 x 45

90 = 3 x 30

90 = 5 x 18

90 = 6 x 15

90 = 9 x 10

Hence possible tiles can be as follows: 1 x 1, 2 x 2, 3 x 3, 5 x 5, 6 x 6, etc.

Since Rani bought the shortest tile, Geetha bought the middle-sized one and Naseema bought the longest one, different possible sizes can be selected as follows:

• (i) Rani takes tiles of size
  = 1 foot × 1 foot
  Geetha takes tiles of size
  = 2 feet × 2 feet
  Naseema takes tiles of size
  = 3 feet × 3 feet
• (ii) Rani takes tiles of size
  = 2 feet × 2 feet
  Geetha takes tiles of size
  = 3 feet × 3 feet
  Naseema takes tiles of size
  = 5 feet × 5 feet
• (iii) Rani takes tiles of size
  = 3 feet × 3 feet
  Geetha takes tiles of size
  = 5 feet × 5 feet
  Naseema takes tiles of
  = size 6 feet × 6 feet