To analyze whether it is possible to have a horizontal distance of 16 inches given a ramp that is 3 feet (39 inches) long and has a vertical rise of 20 inches, we can use the Pythagorean theorem.
In this case, we can represent the situation as a right triangle where:
- The length of the ramp is the hypotenuse (3 feet = 39 inches).
- The vertical rise is one leg of the triangle (20 inches).
- The horizontal distance is the other leg of the triangle (we want to determine if this distance can be 16 inches).
According to the Pythagorean theorem:
\[ \text{(horizontal distance)}^2 + \text{(vertical rise)}^2 = \text{(length of ramp)}^2 \]
Substituting the known values:
Let \( x \) be the horizontal distance:
\[ x^2 + 20^2 = 39^2 \]
Calculating \( 20^2 \) and \( 39^2 \):
\[ x^2 + 400 = 1521 \]
Now, solve for \( x^2 \):
\[ x^2 = 1521 - 400 \] \[ x^2 = 1121 \] \[ x = \sqrt{1121} \approx 33.5 \text{ inches} \]
Now we can see that the maximum possible horizontal distance, based on the length of the ramp and the vertical rise, is approximately 33.5 inches, which is greater than 16 inches.
Therefore, a horizontal distance of 16 inches is indeed feasible given the constraints provided.
Thus, the best response is:
It is possible because 3 feet is 39 inches and the horizontal distance can indeed be 16 inches given the vertical rise of 20 inches.