The length of a rectangle is the sum of the width and 1. The area of the rectangle is 72 square units. What is the length, in units, of the rectangle?
Let's denote the width of the rectangle as W.
According to the given information, the length of the rectangle is the sum of the width and 1, so the length is W + 1.
The area of a rectangle is calculated by multiplying the length and width, so:
Area = Length x Width
72 = (W + 1) x W
72 = W^2 + W
Since we know the area is 72, we can rearrange the equation to be a quadratic equation:
W^2 + W - 72 = 0
Now we need to factorize this equation to find the values of W. The factors of 72 that could add up to 1 are 9 and 8. Therefore, the factors are (W + 9)(W - 8) = 0.
This gives us two possibilities, W = -9 or W = 8. Since W, the width, can't be negative, the width of the rectangle is 8 units.
Therefore, the length of the rectangle is W + 1 = 8 + 1 = 9 units.