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.

Question

(1 point)
teet

Answer 1

To find the length of the ramp, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the ramp, in this case) is equal to the sum of the squares of the lengths of the other two sides (the height of the ramp and the horizontal distance).

In this example, we have:

• Height of the ramp (one side) = 6 feet
• Horizontal distance (the other side) = 8 feet

Let \( L \) be the length of the ramp (the hypotenuse). According to the Pythagorean theorem:

\[ L^2 = (height^2) + (horizontal\ distance^2) \]

Substituting the values we have:

\[ L^2 = (6^2) + (8^2) \] \[ L^2 = 36 + 64 \] \[ L^2 = 100 \]

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

\[ L = \sqrt{100} = 10 \]

Thus, the length of the ramp is 10 feet.