Question

A wheelchair ramp is constructed to rise 3 feet off the ground and extends 4 feet along the ground. How long will the wheelchair ramp be?

Answer 1

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**.