Question

working with the pythagorean theorem: part 2
1 more question to go
an engineer is designing a wheelchair ramp. it needs to rise 3 feet over a horizontal distance of 5 feet. accessibility standards state the inclined surface of the ramp must be at least 6 feet long. does the ramp meet the standard? why or why not?
the ramp does not meet the standard, because its inclined surface will be between 5 and 6 feet long.
the ramp meets the standard because its inclined surface will be 17 feet long.
the ramp meets the standard because its inclined surface will be 8 feet long.

Explanation:

Step1: Apply Pythagorean theorem

The ramp forms a right triangle with vertical leg $a=3$ ft and horizontal leg $b=5$ ft. The inclined surface is the hypotenuse $c$, so $c = \sqrt{a^2 + b^2}$.

Step2: Calculate hypotenuse length

$c = \sqrt{3^2 + 5^2} = \sqrt{9 + 25} = \sqrt{34} \approx 5.83$ ft.

Step3: Compare with standard

The standard requires at least 6 ft. Since $5.83 < 6$, the ramp does not meet the standard.

Answer:

The ramp does not meet the standard, because its inclined surface will be between 5 and 6 feet long.