135k views
2 votes
The length of a rectangle is the sum of the width and 1. The area of the rectangle is 30 units. What is the length, in units, of the rectangle?.

1 Answer

7 votes

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

User Kartos
by
7.8k points