Question

4C. Quintin is using the three different shaped
tiles shown to tile his kitchen floor:
Each tile is composed of 5 identical squares
and has an area of 2000 square centimetres.
The floor is a rectangle 10 metres long and 6 metres wide.
What is the smallest number of tiles Quintin will need in order to tile
his floor?

Answer 1

The smallest number of tiles Quintin will need in order to tile  his floor is 20

The given parameters;

• number of different shapes of tiles available = 3

• number of each shape = 5

• area of each square shape tiles, A = 2000 cm²

• length of the floor, L = 10 m = 1000 cm

• width of the floor, W = 6 m = 600 cm

To find:

• the smallest number of tiles Quintin will need in order to tile his floor

Among the three different shapes available, total area of one is calculated as;

$A_{one \ square \ type} = 5 \times 2000 \ cm^2 = 10,000 \ cm^2$

Area of the floor is calculated as;

$A_{floor} = 1000 \ cm \times 600 \ cm = 600,000 \ cm^2$

The maximum number tiles needed (this will be possible if only one shape type is used)

$maximum \ number= \frac{Area \ of \ floor}{total \ area \ of \ one \ shape \ type} \\\\maximum \ number= \frac{600,000 \ cm^2}{10,000 \ cm^2} \\\\maximum \ number= 60$

When all the three different shape types are used we can get the smallest number of tiles needed.

The minimum or smallest number of tiles needed (this will be possible if all the 3 different shapes are used)

$3 \times \ smallest \ number = 60\\\\smallest \ number = \frac{60}{3} \\\\smallest \ number = 20$

Thus, the smallest number of tiles Quintin will need in order to tile  his floor is 20

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