Answer:
The width of the rectangle is 5 units, and the length is w + 1 = 5 + 1 = 6 units
Explanation:
1) Let's call the width of the rectangle "w" units. According to the given information, the length is the sum of the width and 1, so the length is w + 1 units.
2) The formula for the area of a rectangle is length times width, so in this case, it would be:
w(w + 1) = 30
3) Now, let's solve for "w":
w^2 + w = 30
4) To solve this quadratic equation, we can rearrange it and set it equal to zero:
w^2 + w - 30 = 0
5) Now, we can factor this equation:
(w + 6) (w - 5) = 0
6) Setting each factor equal to zero gives us two possible solutions:
w + 6 = 0 which means w = −6 (but negative width doesn't make sense in this context).
w - 5 = 0 which means w = 5
7) So, the width of the rectangle is 5 units, and the length is w + 1 = 5 + 1 = 6 units