Final answer:
To find the value of x in a rectangle with given dimensions and area, we set up an equation using the formula for the area of a rectangle and solve for x. In this case, the value of x is 11ft.
Step-by-step explanation:
To find the value of x, we need to use the formula for the area of a rectangle, which is length multiplied by width. In this case, the length is (x+5)ft and the width is (x-7)ft. So the equation is (x+5)(x-7) = 64.
To solve this equation, we can expand the brackets and simplify: x^2 - 2x - 35 = 64. Rearranging, we get x^2 - 2x - 99 = 0. Factoring or using the quadratic formula, we find that x = -9 or x = 11.
However, since the dimensions of a rectangle cannot be negative, the value of x is 11ft.