To find the length of the wheelchair ramp, we can use the Pythagorean theorem. In this situation, the ramp forms a right triangle where the rise (height) is one leg, the distance along the ground (base) is the other leg, and the ramp itself is the hypotenuse.
Let's denote:
- the height (rise) as \( a = 3 \) feet,
- the base (distance along the ground) as \( b = 4 \) feet,
- the length of the ramp (hypotenuse) as \( c \).
According to the Pythagorean theorem: \[ c^2 = a^2 + b^2 \]
Substituting the values we have: \[ c^2 = 3^2 + 4^2 \] \[ c^2 = 9 + 16 \] \[ c^2 = 25 \]
Now, take the square root of both sides: \[ c = \sqrt{25} = 5 \]
Thus, the length of the wheelchair ramp is 5 feet.