Question

The length of a ramp is 3 feet long and its vertical rise is 20 inches. Explain why it is or is not possible to have a horizontal distance of 16 inches.

Answer 1

To determine whether a ramp that is 3 feet long with a vertical rise of 20 inches can have a horizontal distance of 16 inches, we can use the Pythagorean theorem. The ramp creates a right triangle where:

- The length of the ramp is the hypotenuse (c).
- The vertical rise is one leg of the triangle (a).
- The horizontal distance is the other leg of the triangle (b).

First, we need to convert all measurements to the same units. The length of the ramp is given as 3 feet, which we convert to inches:
\[
3 \text{ feet} \times 12 \text{ inches/foot} = 36 \text{ inches}
\]

So we have:
- Hypotenuse (c) = 36 inches
- Vertical rise (a) = 20 inches
- Horizontal distance (b) = ?

Now, according to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
Substituting the known values:
\[
36^2 = 20^2 + b^2
\]
Calculating the squares:
\[
1296 = 400 + b^2
\]

Now, solve for \(b^2\):
\[
b^2 = 1296 - 400
\]
\[
b^2 = 896
\]

Taking the square root of both sides to find \(b\):
\[
b = \sqrt{896}
\]
Calculating \(b\):
\[
b \approx 29.98 \text{ inches}
\]

Since \(b \approx 29.98\) inches is greater than 16 inches, it confirms that having a horizontal distance of only 16 inches is indeed impossible. Therefore, it is not possible for a ramp that is 3 feet long and has a vertical rise of 20 inches to have a horizontal distance of 16 inches. The horizontal distance must be approximately 29.98 inches.