Final answer:
The perimeter of the isosceles triangle is composed of the base and two equal legs. With the given perimeter of 122, the base being x, and the legs as 5x-5, we solved the equation 122 = x + (5x-5) + (5x-5) to find that x is 12.45.
Step-by-step explanation:
The perimeter P of an isosceles triangle is the sum of the lengths of its three sides.
Given that the base length is x, and the length of each of the equal legs is 5x-5, we can write the perimeter equation as:
P = x + (5x-5) + (5x-5)
Since the perimeter P is given to be 122:
122 = x + (5x-5) + (5x-5)
122 = x + 10x - 10 - 5
Now, simplifying the equation:
122 = 11x - 15
Adding 15 to both sides:
137 = 11x
Dividing both sides by 11:
x = 12.45 (rounded to two decimal places)
So, the value of x is 12.45.