Most new buildings are required to have a ramp for the handicapped that has a maximum vertical rise of 11 feet for every 132 feet of horizontal distance. A. m= (Simplify your answer.) boxes within your choice. B. The slope is undefined. (b) If the builder constructs a new building in which the ramp has a horizontal distance of 48 feet, what is the maximum height of the doorway above the level of the parking lot where the ramp begins? \( \square \) feet (Type an integer or decimal rounded to one decimal place.) (c) What is the shortest possible distance between the building and the end of the ramp if the architect redesigns the building so that the doorway is 1.9 feet above the parking lot? feet the correct choice below and fill in any answer feet (Type an integer or decimal rounded to one decimal place.)

To solve the problem, we will break it down into parts A, B, and C. ### Part A: Finding the slope (m) The slope \( m \) is defined as the ratio of the vertical rise to the horizontal run. Given that the maximum vertical rise is 11 feet for every 132 feet of horizontal distance, we can express this as: \[ m = \frac{\text{rise}}{\text{run}} = \frac{11}{132} \] Now, we will simplify this fraction. ### Part B: Maximum height of the doorway If the builder constructs a ramp with a horizontal distance of 48 feet, we can use the slope to find the maximum height of the doorway. The slope can be expressed as: \[ \text{slope} = \frac{\text{height}}{\text{horizontal distance}} \] Rearranging this gives us: \[ \text{height} = \text{slope} \times \text{horizontal distance} \] We will calculate the maximum height using the slope we found in Part A. ### Part C: Shortest possible distance between the building and the end of the ramp If the doorway is 1.9 feet above the parking lot, we can use the same slope to find the horizontal distance required for this height. Rearranging the slope formula gives us: \[ \text{horizontal distance} = \frac{\text{height}}{\text{slope}} \] We will calculate this distance using the height of 1.9 feet. Now, let's perform the calculations for parts A, B, and C. ### Step 1: Calculate the slope (m) and simplify it \[ m = \frac{11}{132} \] ### Step 2: Calculate the maximum height for a horizontal distance of 48 feet \[ \text{height} = m \times 48 \] ### Step 3: Calculate the horizontal distance for a height of 1.9 feet \[ \text{horizontal distance} = \frac{1.9}{m} \] Let's perform these calculations. Calculate the value by following steps: - step0: Calculate: \(\frac{11}{132}\) - step1: Reduce the fraction: \(\frac{1}{12}\) Calculate or simplify the expression \( 1.9 / (11/132) \). Calculate the value by following steps: - step0: Calculate: \(\frac{1.9}{\left(\frac{11}{132}\right)}\) - step1: Remove the parentheses: \(\frac{1.9}{\frac{11}{132}}\) - step2: Reduce the fraction: \(\frac{1.9}{\frac{1}{12}}\) - step3: Convert the expressions: \(\frac{\frac{19}{10}}{\frac{1}{12}}\) - step4: Multiply by the reciprocal: \(\frac{19}{10}\times 12\) - step5: Reduce the numbers: \(\frac{19}{5}\times 6\) - step6: Multiply: \(\frac{19\times 6}{5}\) - step7: Multiply: \(\frac{114}{5}\) Calculate or simplify the expression \( (11/132) * 48 \). Calculate the value by following steps: - step0: Calculate: \(\left(\frac{11}{132}\right)\times 48\) - step1: Reduce the fraction: \(\frac{1}{12}\times 48\) - step2: Reduce the numbers: \(1\times 4\) - step3: Simplify: \(4\) ### Part A: Finding the slope (m) The slope \( m \) is simplified as follows: \[ m = \frac{11}{132} = \frac{1}{12} \] ### Part B: Maximum height of the doorway Using the slope to find the maximum height for a horizontal distance of 48 feet: \[ \text{height} = m \times 48 = \frac{1}{12} \times 48 = 4 \text{ feet} \] ### Part C: Shortest possible distance between the building and the end of the ramp Using the height of 1.9 feet to find the horizontal distance: \[ \text{horizontal distance} = \frac{1.9}{m} = \frac{1.9}{\frac{1}{12}} = 1.9 \times 12 = 22.8 \text{ feet} \] ### Summary of Answers: - **Part A:** \( m = \frac{1}{12} \) - **Part B:** The maximum height of the doorway is \( 4 \) feet. - **Part C:** The shortest possible distance between the building and the end of the ramp is \( 22.8 \) feet.