Question

most new buildings are required to have a ramp for the handicapped that has a maximum vertical rise of 6 feet for every 72 feet of horizontal distance.
(b) if the builder constructs a new building in which the ramp has a horizontal distance of 132 feet, what is the maximum height of the doorway above the level of the parking lot where the ramp begins?
(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 12 feet above the parking lot?
(type an integer or decimal rounded to one decimal place.)
(type an integer or decimal rounded to one decimal place.)

Explanation:

Step1: Recall slope - formula

The slope formula for a ramp is $m=\frac{\text{vertical rise}}{\text{horizontal run}}$. The maximum slope $m$ for a handicap - accessible ramp is $\frac{6}{72}=\frac{1}{12}$.

Step2: Solve for vertical rise in part (b)

We know the horizontal distance (run) $x = 132$ feet and $m=\frac{1}{12}$. Using the slope formula $m=\frac{y}{x}$, we can solve for $y$ (vertical rise). Substituting the values, we get $\frac{1}{12}=\frac{y}{132}$. Cross - multiply: $y=\frac{132}{12}=11$ feet.

Step3: Solve for horizontal run in part (c)

We know the vertical rise $y = 12$ feet and $m=\frac{1}{12}$. Using the slope formula $m=\frac{y}{x}$, we can solve for $x$ (horizontal run). Cross - multiply: $x = 12\times12=144$ feet.

Answer:

(b) 11 feet
(c) 144 feet