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) What is the value of the slope of a ramp for the handicapped? Select the correct choice below and fill in any answ boxes within your choice. A. \( m=\square \) (Simplify your answer.) 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 maximur 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? \( \square \) feet (Type an integer or decimal rounded to one decimal place.)

**(a)** The ramp has a maximum vertical rise of \( 11 \) feet over a horizontal distance of \( 132 \) feet. The slope \( m \) is given by \[ m=\frac{\Delta y}{\Delta x}=\frac{11}{132}. \] Simplify by dividing numerator and denominator by \( 11 \): \[ m=\frac{1}{12}. \] **(b)** If the horizontal distance is \( 48 \) feet, the maximum vertical rise \( h \) is found by \[ h=m\times 48=\frac{1}{12}\times 48=4 \text{ feet}. \] **(c)** When the doorway is \( 1.9 \) feet above the parking lot, the ramp must rise \( 1.9 \) feet at a maximum slope of \( \frac{1}{12} \). The required horizontal distance is \[ d=12\times 1.9=22.8 \text{ feet}. \] The actual (shortest) distance along the ramp (the hypotenuse of the right triangle formed by the horizontal and vertical legs) is \[ L=\sqrt{d^2 + (1.9)^2}=\sqrt{(22.8)^2 + (1.9)^2}. \] Calculate the squares: \[ (22.8)^2=519.84,\quad (1.9)^2=3.61, \] so, \[ L=\sqrt{519.84+3.61}=\sqrt{523.45}\approx22.9 \text{ feet}. \] Thus, the answers are: (a) \( m=\frac{1}{12} \) (b) \( 4 \) feet (c) \( 22.9 \) feet