Final answer:
To find the length of AB, set AB equal to AC and solve for x. Substitute the value of x back into AB to find the length.
Step-by-step explanation:
To find the length of AB, we need to equate AB to a known value and solve for x. We are given that AB = 4x + 15, BC = 2x - 10, and AC = 77. Since AB and AC are two sides of the same triangle, we can set them equal to each other: 4x + 15 = 77. Solving this equation, we get 4x = 62 and x = 15.5. Substituting this value back into AB = 4x + 15, we find that AB = 4(15.5) + 15 = 61.