Answer:
x = 12
Explanation:
We are given that the dimensions of a rectangle are (x-1) and (x+7) meters, and we know that the area of the rectangle is 128 square meters.
We can set up an equation to solve for x as follows:
Area of rectangle = Length × Width
128 = (x-1)(x+7)
Expanding the right side, we get:
128 = x^2 + 6x - 7
Bringing all the terms to one side, we get:
x^2 + 6x - 135 = 0
Now we can use the quadratic formula to solve for x:
x = (-6 ± √(6^2 - 4(1)(-135))) / (2(1))
x = (-6 ± √936) / 2
x = (-6 ± 30) / 2
x = -3 ± 15
x = -18 or x = 12
Since x represents a length, it must be positive. Therefore, the value of x is 12.