A tiler has 100 square tiles for tiling two square panels in a bathroom. Explain why the panels cannot be of the same size. Each tile is \( 10 \times 10 \mathrm{~cm} \). What are the dimensions of the two square panels if all 100 tiles are used?
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If the two panels were of the same size, each would have an area of 5000 cm² (10000 cm² / 2). However, the side length of a square is the square root of its area, and the square root of 5000 is not a whole number. Show more…
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Solve the problem posed at the beginning of the lesson. An artist uses 200 tiles to create a tessellation design that covers a rectangle with dimensions $2 \mathrm{ft}$ by $3 \mathrm{ft}$. He will cover a wall with dimensions $10 \mathrm{ft}$ by $15 \mathrm{ft}$ using the same design and tiles of the same size. How many tiles will he need to cover the entire wall?
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