Area=432
width is 6 feet less than length. what's the length.
I haven't done this since the beginning of the year so I could really use the help remembering how.
length ---- x
width ------ x-6
x(x-6) = 432
x^2 - 6x - 432 = 0
solve as a quadratic. hint: it factors, but the quadratic formula will
also give you the answer.
Personally, I would have completed the square.
To find the length when given the area and the relationship between the width and the length, you can set up an equation based on the given information, then solve for the length.
Let's denote the length as "L." We are given that the width is 6 feet less than the length, so we can represent the width as "L - 6."
The formula for the area of a rectangle is A = length × width. In this case, the given area is 432, so we have the equation:
432 = L × (L - 6)
Now, let's solve for L.
Expanding the equation, we get:
432 = L^2 - 6L
Rearranging the equation, we have:
L^2 - 6L - 432 = 0
To solve this quadratic equation, you can either factor it or use the quadratic formula. Since it's not easily factorable, let's use the quadratic formula:
L = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -6, and c = -432. Plugging in these values, we can calculate the length as follows:
L = (-(-6) ± √((-6)^2 - 4(1)(-432))) / (2(1))
= (6 ± √(36 + 1728)) / 2
= (6 ± √(1764)) / 2
= (6 ± 42) / 2
Now we have two possible values for L:
L = (6 + 42) / 2 or L = (6 - 42) / 2
Simplifying these equations, we get:
L = 48 / 2 or L = -36 / 2
= 24 or L = -18
Since the length of a rectangle cannot be negative, the length, in this case, is 24 feet.
Therefore, the length of the rectangle is 24 feet.