when the length of a rectangle with a width of 1/6ft was increased by 2/3ft, the area of the rectangle became 11/72 sq ft. what was the original length

1/4 ft

Step-by-step explanation:

The area is given by the product of length and width. Since the width of the rectangle was not changed, the new length L satisfies the equation ...

(1/6 ft) ·L = 11/72 ft²

Multiplying by 6/ft tells us the new length:

L = (6/ft) ·11/72 ft² = 11/12 ft

The original length is 2/3 ft shorter so is ...

L - 2/3 ft = 11/12 ft - 8/12 ft = 3/12 ft

L = 1/4 ft