Question

We paved a square room with rectangular tiles measuring 20 cm by 30 cm. An integerof slabs was used.Find the length of the side of the smallest square piece that can be paved if the length of theside of the square is between 4.5 m and 5 m. Determine the number of tiles used.

Answer 1

The length of the smallest side = 4.8 m

The number of tiles used is 384.

Step-by-step explanation:

The situation is explained in the drawing below (the number total of tiles is not represented in the figure):

From the question, we know:

* The paved room is a square

* An integer number of tiles was used.

Let say "a" is the measure of the sides of the squares, "a" has to be divisible by 20 and 30.

So, let's test the numbers between 450 and 500 cm.

To be divisible by 20 and 30, the number has to end with 0. So, we have the options 450, 460, 470, 480, ....

450/20 = 22.5

Since it is not an integer, 450 is not the answer.

460/20 = 23

460/30 = 15.33

Since it is not an integer, 460 is not the answer.

470/20 = 23.5

Since it is not an integer, 470 is not the answer.

480/20 = 24

480/30 = 16

So, 480 cm, or 4.8 m is the smallest length of the side that can be paved.

And the number of tiles used is 24*16 = 384