An incline ramp on a moving van measures 196 inches. The height of the moving van to the ground is 32 inches. What is the longest distance that the ramp can be extended (the distance from back of the truck to the edge of the ramp when the ramp is at rest on the ground)?

Question

Round your answer to the nearest whole number.

Answer 1

Let's call the longest distance that the ramp can be extended $x$.

If we draw a right triangle with the incline ramp representing the hypotenuse, the height of the moving van representing one of the legs, and $x$ representing the other leg, we can use the Pythagorean theorem to find $x$.

The Pythagorean theorem states that for a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

So, we have:

$x^2 + 32^2 = 196^2$

$x^2 + 1024 = 38416$

$x^2 = 38416 - 1024$

$x^2 = 37492$

Taking the square root of both sides, we find:

$x = \sqrt{37492} \approx 193.6$

Rounding to the nearest whole number, the longest distance that the ramp can be extended is 194 inches.