Answer:
length: 14.2 ft; width 4.2 ft.
Step-by-step explanation:
Let x represent the length of the rectangle in feet. Then x-10 represents the width, and the area is ...
area = length×width
60 = x(x -10) . . . . . substitute the expressions for area, length, width
60 = x² -10x
85 = x² -10x +25 . . . . add (10/2)² to complete the square
85 = (x -5)² . . . . . . . . . rewrite as a square
√85 = x -5 . . . . . . . . . take the square root. Only the positive root is useful for this problem
x = 5 + √85 ≈ 14.2
x-10 = 4.2
The length and width of the rectangle are 14.2 ft and 4.2 ft.
