# Ms Perea's kitchen floor is a rectangle with the dimensions 12.5 ft \times 22.5 ft. She wants to cover the floor with rectangular tiles that measure 1.5 ft \times 0.8 ft. How many tiles will she need to cover the kitchen floor?

Jan 9, 2018

It is all down to the most efficient use of tiles and utilising off cuts.

Diagram 1 $\to 224 \text{ total tiles utilising 19 recycled tile parts.}$
Diagram 2 $\to 240 \text{ total tiles with no recycled tile parts}$

Diagram 1 is able to recycle more of the off cuts so less wastage

#### Explanation:

Don't forget that you can not purchase part of a tile. So it may be the case that some will have to be cut to fit.

The question does not state what type the tiles they are. If ceramic then in real life there will be gaps between them.

Assuming no gaps between tiles.

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$\textcolor{b r o w n}{\text{Testing for exact fit using "1.5" feet}}$

$12.5 \div 1.5 = 8.3 \overline{3} \to 8 \frac{1}{3}$ tiles. So each strip will lose $\frac{2}{3}$ of a tile.

$22.5 \div 1.5 = 15$ An exact fit
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$\textcolor{b r o w n}{\text{Testing for exact fit using "0.8" feet}}$

$12.5 \div 0.8 = 15.625 \to 15 \frac{5}{8}$ tiles. So each strip will lose $\frac{3}{8}$ of a tile. Note that the remainder of the cut tile is not usable so it is scrap.

$22.5 \div 0.8 = 28.125 \to 28 \frac{1}{8}$ so each strip will lose $\frac{7}{8}$ of a tile.
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$\textcolor{b r o w n}{\text{Determining which combination uses the least tiles "->" costs less}}$

$\textcolor{m a \ge n t a}{\text{Diagram 1}}$

$\textcolor{m a \ge n t a}{\text{Diagram 2}}$