Final answer:
To find the value of x for the isosceles triangle with a given perimeter of 69, we set up the equation x + 2(5x - 4) = 69 and solve for x, yielding a value of 7.
Step-by-step explanation:
The student needs to find the value of x given that the base of an isosceles triangle is x, the length of a leg is 5x-4, and the perimeter of the triangle is 69.
Since the triangle is isosceles, both legs are of equal length.
Therefore, the perimeter of the triangle is the base plus twice the length of one leg, which is given by the equation:
x + 2(5x - 4) = 69
Solving for x:
x + 10x - 8 = 69
11x - 8 = 69
11x = 69 + 8
11x = 77
x = 77/11
x = 7
Therefore, the value of x is 7.