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Designing a Rectangular Patio with Mat and Border: Tile Calculations

In this exercise, Kenneth is planning to tile a rectangular patio area with rectangular tiles. He wants the number of tiles on each side to be equal. The patio will feature a central mat, surrounded by a 6-inch border. The dimensions of the mat are defined by the functions L(x) = 12x - 12 and W(x) = 6x - 12, where x is the number of tiles on each side. The task includes determining specific values of L and W, explaining their significance, and calculating the area of the mat based on a total of 100 tiles used.

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Designing a Rectangular Patio with Mat and Border: Tile Calculations

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  1. M3309-F10 Week 11.2 F F(x) x + F(x) + G(x) G G(x)

  2. M3309-F10 Week 11.2 6 24 18 42 F 24 6 + 42 G 18

  3. M3309-F10 Week 11.2 6 6 432 24 18 42 F 24 6 1.3 1.3  G 18

  4. M3309-F10 Week 11.2 6 6 432 24 18 42 k 4k 2k + 6 6k + 6 F 4k k 1.3 + 6k + 6 G 2k + 6

  5. M3309-F10 Week 11.2 6 6 432 24 18 42 k 4k 2k + 6 6k + 6 2k – 6 F 4k k 1.3 – 4k – (2k + 6) G 2k + 6

  6. M3309-F10 Week 11.2 6 6 432 24 18 42 k 4k 2k + 6 6k + 6 2k – 6 8k2+ 24k F 4k k 1.3  4k(2k + 6) G 2k + 6

  7. M3309-F10 Week 11.2 C(n) R(n)

  8. M3309-F10 Week 11.2 C(n) R(n) P(n)

  9. M3309-F10 Week 11.2 C(n) R(n) P(n)

  10. M3309-F10 Week 11.2 2. Kenneth is planning to tile a rectangular area for his patio. He plans to use rectangular tiles but he wants the number of tiles on the longer side to be the same as the number of tiles on the shorter side. He plans to cover the center of the patio with an outdoor mat, leaving a border of 6 inches around the mat. The length and width of the mat, in number of inches, are given by functions L(x) = 12x – 12 and W(x) = 6x – 12 respectively, where the input x represents the number of tiles on each side.(The diagram represents a patio with 4 tiles on each side.) 6 in. 6 in. • a. Find L(15). Explain what L(15) represents. • b. Find W(15). Explain what the number 6 and the number 12 in W(x) = 6x – 12 represent.

  11. M3309-F10 Week 12.2 2. Kenneth is planning to tile a rectangular area for his patio. He plans to use rectangular tiles but he wants the number of tiles on the longer side to be the same as the number of tiles on the shorter side. He plans to cover the center of the patio with an outdoor mat, leaving a border of 6 inches around the mat. The length and width of the mat, in number of inches, are given by functions L(x) = 12x – 12 and W(x) = 6x – 12 respectively, where the input x represents the number of tiles on each side.(The diagram represents a patio with 4 tiles on each side.) 6 in. 6 in. • c. If Kenneth uses a total of 100 tiles, what is the area of the mat? Explain the steps you took to find the answer.

  12. M3309-F10 Week 12.2 L(x) 1 0 0 2 0 0 W(x)

  13. M3309-F10 Week 12.2 L(x) 1 0 0 2 0 0 1.5 -18 6 -3 W(x)

  14. M3309-F10 Week 12.2 L(x) 1 0 0 2 0 0 1.5 -18 6 -3 2.2 17.28 14.4 1.2 W(x) 0.8 17.28 -2.4 -7.2

  15. M3309-F10 Week 12.2 L(x)W(x) L(x) 1 0 0 2 0 0 1.5 -18 6 -3 2.2 17.28 14.4 1.2 W(x) 0.8 17.28 -2.4 -7.2

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