Final answer:
The side lengths 10.5, 36, and 5 do not form a right triangle as they do not satisfy the Pythagorean theorem, which states that the square of the hypotenuse must equal the sum of the squares of the other two sides.
Step-by-step explanation:
To determine whether the side lengths 10.5, 36, and 5 form a right triangle, we can apply the Pythagorean theorem. According to the theorem, for a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two other sides (a and b). The formula is a² + b² = c², where c is the longest side.
Let's check if 10.5² + 5² equals 36²:
- 10.5² = 110.25
- 5² = 25
- 36² = 1296
Now, let's add the squares of the shorter sides:
110.25 + 25 = 135.25
Since 135.25 does not equal 1296, the side lengths 10.5, 36, and 5 do not satisfy the Pythagorean theorem for a right triangle. Therefore, the answer is:
B) No, they do not form a right triangle.