Question

Tyrese buys potting soil every January to plant vegetables in his garden. This year he bought 15 25-pound bags of potting soil. He must push them up a 6- foot-high ramp to his truck. The horizonal distance from the base of the ramp to the truck is 8 feet. Apply a Pythagorean triple to find the length of the ramp.(1 point)

Answer 1

To find the length of the ramp using the Pythagorean theorem, we can represent the ramp as the hypotenuse of a right triangle, where one leg is the height of the ramp (6 feet) and the other leg is the horizontal distance (8 feet).

The Pythagorean theorem states that:

\[
a^2 + b^2 = c^2
\]

where \(a\) and \(b\) are the lengths of the legs of the triangle, and \(c\) is the length of the hypotenuse (the ramp in this case).

In this scenario:
- \(a = 6\) feet (the height)
- \(b = 8\) feet (the horizontal distance)
- \(c\) is what we want to find (the length of the ramp)

Now substituting the values into the equation:

\[
6^2 + 8^2 = c^2
\]
\[
36 + 64 = c^2
\]
\[
100 = c^2
\]

To find \(c\), we take the square root of both sides:

\[
c = \sqrt{100}
\]
\[
c = 10 \text{ feet}
\]

Thus, the length of the ramp is **10 feet**.