Final answer:
The lengths 15, 10, and 5 do not satisfy the Pythagorean Theorem since the sum of the squares of the shorter two sides (5² + 10² = 125) does not equal the square of the longest side (15² = 225). Therefore, they cannot form a right triangle.
Step-by-step explanation:
To determine if the lengths 15, 10, and 5 satisfy the Pythagorean Theorem, we need to identify which length would be the hypotenuse in a right triangle. The hypotenuse is the longest side, which in this case is 15. The Pythagorean Theorem states that the square of the hypotenuse length (c), should equal the sum of the squares of the other two sides (a and b).
Using the formula: a² + b² = c², let's plug in the lengths:
a=5, b=10, and c=15:
5² + 10² = 15²
25 + 100 = 225
125 ≠ 225
Here we see that 125 does not equal 225. Therefore, the lengths 15, 10, and 5 do not satisfy the Pythagorean Theorem; they would not form a right triangle.