Final answer:
The problem involves solving for the variable x in an isosceles triangle's perimeter formula, given the base length and leg lengths in terms of x and the total perimeter. The equation 144 = x + (5x - 5) + (5x - 5) is simplified to find x = 14.
Step-by-step explanation:
The student's question revolves around solving for a variable in the perimeter formula of an isosceles triangle, where the lengths of the sides of the triangle are given in terms of the variable x. Specifically, the base length is x, and the length of one leg is 5x - 5. Given that the perimeter of the triangle is 144, we are asked to find the value of x.
To solve this, we need to understand that in an isosceles triangle, the two legs are equal. So the perimeter P, which is the sum of all sides of the triangle, is given by:
P = base + leg1 + leg2
Since the base is x, and both legs are 5x - 5, we can write the equation as:
144 = x + (5x - 5) + (5x - 5)
Combining like terms results in:
144 = 11x - 10
Adding 10 to both sides gives us:
154 = 11x
Finally, dividing both sides by 11 yields:
x = 14
Therefore, the value of x is 14.