Rani, Geetha and Naseema live near each other. The distance from their houses to the road is 90 feet. They decided to tile the path to the road. They all bought tiles of different designs and length. Rani bought the shortest tile, Geetha bought the middle sized 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.

Open in App

Solution

Length of the path = 90 feet
Now, they have to choose a size of tile that can be tiled on the path without cutting.
So, size of tile should be a factor of 90.

Factors of 90 are 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45 and 90.
Rani chooses the smallest size tile, Geetha takes the middle sized and Naseema the largest.

So, we can choose the tiles in the following way:

(a) Rani can take tiles of size 1 foot $\times$ 1 foot, Geetha can choose tiles of size 2 feet $\times$ 2 feet, Naseema can buy tiles of size 3 feet $\times$ 3 feet.

(b)Rani can take tiles of size 2 feet $\times$ 2 feet, Geetha can choose tiles of size 3 feet $\times$ 3 feet, Naseema can buy tiles of size 5 feet $\times$ 5 feet.

(c) Rani can take tiles of size 3 feet $\times$ 3 feet, Geetha can choose tiles of size 5 feet $\times$ 5 feet, Naseema can buy tiles of size 6 feet $\times$ 6 feet.

Suggest Corrections

Similar questions

There is a garden in Anu's house. In the middle of the garden there is a path. They decided to tile the path using tiles of length $2$ feet, $3$ feet and $5$ feet.
The mason tiled the first row with $2$ feet tiles, the second row with $3$ feet tiles and the third row with $5$ feet tiles. The mason has not cut any of the tiles. Then what is the shortest length of the path?

Q. A man paved his square courtyard with square tiles. After this, he wanted to increase the courtyard and bought 324 more tiles of the same size. These were added onto the existing courtyard to make a bigger one in square shape. Find the total number of tiles used to make the bigger courtyard.

Q. Manoj has a new house. He to lay tiles on the floor. The size of the room is 9 feet × 12 feet. In the market, there are three kinds of square tiles: 1 feet × 1 feet, 2 feet × 2 feet and 3 feet × 3 feet. Which size of tile should he buy for his room, so that he can lay it without cutting?

You can also make your own tiles and use them to make your own tiling patterns. You will find some such tiles at the end of the book that you can cut out, trace and colour.

Join BYJU'S Learning Program