Final answer:
To find the value of x for an isosceles triangle with a base of x and legs of 4x-7 and a perimeter of 58, we set up an equation and solve for x. By combining like terms and solving, we find that the value of x is 8.
Step-by-step explanation:
To find the value of x for the perimeter of the isosceles triangle, we set up an equation using the given information.
Since the triangle is isosceles, it has two legs that are equal in length.
The base is given as x, and each leg is 4x-7.
The perimeter of the triangle is the sum of the lengths of all its sides.
Therefore, the equation for the perimeter is:
P = base + leg + leg
58 = x + (4x-7) + (4x-7)
Combining like terms, we get:
58 = x + 4x - 7 + 4x - 7
58 = 9x - 14
Adding 14 to both sides, we have:
58 + 14 = 9x
72 = 9x
Dividing both sides by 9, we find:
x = 72 / 9
x = 8
Therefore, the value of x is 8.