The floor of a conference hall can be covered completely with tiles. Its length is 36 ft longer than its width. The area of the floor is less than 2,040 square feet.
1. How would you represent the width of the floor? How about its length?
2. What mathematical sentence would represent the given situation?
3. What are the possible dimensions of the floor? How about the possible areas of the floor? Give at least 3 possible dimensions and areas.
4. Would it be realistic for the floor to have an area of 144 square feet? Explain your answer.
Answer (1)
1. How would you represent the width of the floor? How about its length?Width = xLength = x + 362. What mathematical sentence would represent the given situation?[tex]\mathsf{x(x + 36) < 2040}[/tex]3. What are the possible dimensions and areas?[tex]\mathsf{24 \times (24 + 36) = 24 \times 60 = 1440} \quad \text{✅}[/tex][tex]\mathsf{28 \times (28 + 36) = 28 \times 64 = 1792} \quad \text{✅}[/tex][tex]\mathsf{30 \times (30 + 36) = 30 \times 66 = 1980} \quad \text{✅}[/tex]4. Would it be realistic for the floor to have an area of 144 square feet? Explain your answer.No, it would not be realistic.Even though 144ft² is mathematically possible, it is too small for a conference hall[tex]\mathsf{12 \times 12 = 144}[/tex]
