Question

Tyler buys potting soil every January to plant his vegetable 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 horizontal distance from the base of the ramp to the truck is 8 feet.

use a pythagorean triple to gind the length of the ramp.

Answer 1

To find the length of the ramp that Tyler must push the potting soil up, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case:
- The height of the ramp (the vertical side) is 6 feet.
- The horizontal distance (the other side) is 8 feet.
- We need to find the length of the ramp (the hypotenuse).

Let \( c \) be the length of the ramp (hypotenuse), \( a \) be the height (6 feet), and \( b \) be the horizontal distance (8 feet). According to the Pythagorean theorem:

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

Substituting the values we have:

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

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

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

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