To determine whether a horizontal distance of 16 inches is possible given a ramp that is 3 feet long (39 inches) and has a vertical rise of 20 inches, we can use the Pythagorean theorem. The ramp, horizontal distance, and vertical rise form a right triangle.
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Convert the ramp length from feet to inches:
- 3 feet = 3 × 12 inches = 36 inches
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The vertical rise is already in inches: 20 inches.
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The ramp length (hypotenuse) is 39 inches, not 36 inches. So let's check if a horizontal distance (base, x) of 16 inches is possible with the given vertical rise.
Using the Pythagorean theorem: \[ (horizontal\ distance)^2 + (vertical\ rise)^2 = (length\ of\ ramp)^2 \] \[ x^2 + (20)^2 = (39)^2 \] \[ x^2 + 400 = 1521 \] \[ x^2 = 1521 - 400 \] \[ x^2 = 1121 \] \[ x ≈ 33.5 \text{ inches} \]
Thus, a horizontal distance of approximately 33.5 inches is required for a vertical rise of 20 inches with a ramp length of 39 inches.
Since 16 inches is less than this calculated horizontal distance, it is not possible to have a horizontal distance of 16 inches given the specified vertical rise and ramp length.
The appropriate response would be:
"It is not possible because the required horizontal distance (approximately 33.5 inches) for a vertical rise of 20 inches exceeds 16 inches."
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