Answer:
length = 10 units; width = 3 units
Explanation:
Let the width = w
Then the length is w + 7
Original area: w(w + 7)
Double the width: 2w
Increase the length by 2: w + 9
Area of new rectangle: 2w(w + 9)
Area of new rectangle = w(w + 7) + 42
2w(w + 9) = w(w + 7) + 42
2w^2 + 18w = w^2 + 7w + 42
w^2 + 11w - 42 = 0
(w + 14)(w - 3) = 0
w + 14 = 0 or w - 3 = 0
w = -14 or w = 3
A width cannot be negative, so we discard w = -14.
The original width is 3 units.
The length is 7 more than the width, so the length is 10 units.