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 horizontal distance from the base of the ramp to the truck is 8 feet. Apply a Pythagorean triple to find he length of the ramp
To apply a Pythagorean triple, we need to find two numbers that can form a right triangle with the given 6-foot height and 8-foot horizontal distance.
A well-known Pythagorean triple is the 3-4-5 triple. We can multiply each of these numbers by 2 to get a multiple of this triple. Therefore, we can use the 6-8-10 triple.
In this case, the length of the ramp (hypotenuse) is the unknown. We can use the Pythagorean theorem, which states that the square of the hypotenuse (c^2) is equal to the sum of the squares of the other two sides (a^2 + b^2).
Let's denote the length of the ramp as 'c'. Using the 6-8-10 triple, we have:
c^2 = 6^2 + 8^2
c^2 = 36 + 64
c^2 = 100
c = √100
c = 10
Therefore, the length of the ramp is 10 feet.