Final answer:
To find the length of AB, we can use the fact that the length of AB is six times the length of BC. By substituting the values into the Pythagorean theorem equation, we can find the length of BC and then calculate the length of AB.
Step-by-step explanation:
To find the length of AB, we can use the fact that the length of AB is six times the length of BC. Let's assume the length of BC is x. Therefore, the length of AB is 6x.
Given that AC is 98, we can use the Pythagorean theorem to find the length of BC. AC^2 = AB^2 + BC^2. Substituting the values, we get 98^2 = (6x)^2 + x^2.
Simplifying the equation, we get 9604 = 36x^2 + x^2. Combining like terms, we get 37x^2 = 9604.
Dividing both sides by 37, we get x^2 = 260. Taking the square root of both sides, we get x = ±√260. Since the length cannot be negative, the length of BC is √260. Therefore, the length of AB is 6 times √260.