23. CEMENT You pour cement in a rectangular region of a square garage. The area of the rectangular region is 112 square feet. s ft a. What is the area of the garage floor? b. You place caution tape along the two sides of the newly cemented region that are not on the wall. How many feet of caution tape do you use?

To solve the problem, let's extract the known conditions and then proceed step by step. ### Known Conditions: 1. The area of the rectangular region where cement is poured is \(112\) square feet. 2. The region is located in a square garage. ### Step-by-Step Solution: #### Part a: Area of the Garage Floor Since the problem states that the rectangular region is in a square garage, we need to find the area of the garage floor. Let \(s\) be the side length of the square garage. The area \(A\) of a square is given by the formula: \[ A = s^2 \] However, we do not have the value of \(s\) directly. The area of the rectangular region does not provide enough information to determine the area of the garage unless we know the dimensions of the rectangular region or the side length of the garage. Since the area of the rectangular region is \(112\) square feet, we can express the area of the garage as: \[ A_{\text{garage}} = s^2 \] Without additional information about the dimensions of the rectangular region or the side length of the garage, we cannot calculate the exact area of the garage. #### Part b: Caution Tape Length Next, we need to determine how much caution tape is used along the two sides of the rectangular region that are not against the wall. Let’s denote the length and width of the rectangular region as \(l\) and \(w\) respectively. The area of the rectangle is given by: \[ l \times w = 112 \] The caution tape will be placed along the two sides that are not against the wall, which means we need to add the lengths of these two sides: \[ \text{Caution Tape Length} = l + w \] To find \(l + w\), we can use the relationship between the area and the dimensions: \[ l + w = \frac{112}{w} + w \] However, without specific values for \(l\) and \(w\), we cannot calculate the exact length of the caution tape. ### Conclusion 1. **Area of the garage floor**: Cannot be determined without additional information about the dimensions of the rectangular region or the side length of the garage. 2. **Length of caution tape**: Cannot be determined without specific values for the dimensions \(l\) and \(w\). If you have any additional information about the dimensions of the rectangular region or the side length of the garage, please provide it so we can proceed with the calculations.