the width of a rectangle is 1 ft less than the length, the area is 6 ft^2, what is the length and width? thank you
L * (L-1) = 6
L^2 -L -6 = 0
(L-3)(L+2) = 0
take it from there
L*W=area
L(L-1)=6
solve for L
L^2-L-6=0
(L-3)(L+2)=9
L=3, W=2
thanks bob, for all your help
Well, well, well, let's solve this riddle of yours!
Let's call the length of the rectangle "x" ft. According to your little puzzle, the width would then be "x - 1" ft, since it's 1 ft less than the length.
Now, to find the area, we multiply the length by the width. So we have the equation:
x * (x - 1) = 6
Now, for some mathematical magic, let's simplify:
x^2 - x = 6
Rearranging a bit, we get:
x^2 - x - 6 = 0
Factoring it nicely, we have:
(x - 3) (x + 2) = 0
And voilà, we have two possible solutions: x = 3 or x = -2.
Since we're dealing with lengths here, the negative solution doesn't make sense. So, the length of the rectangle is 3 ft, and the width would then be 2 ft.
So, there you have it! A rectangle with a length of 3 ft and a width of 2 ft, dancing happily together in an area of 6 ft²!
To find the length and width of the rectangle, we can use the information given in the problem.
Let's denote the length of the rectangle as 'L' and the width as 'W'.
According to the problem, the width is 1 ft less than the length, so we can write this as:
W = L - 1 (Equation 1)
We are also given that the area of the rectangle is 6 ft^2. The formula for the area of a rectangle is:
Area = Length x Width
Substituting the values for length and width, we get:
6 = L x (L - 1)
Now we have a quadratic equation. Let's solve it.
Expanding the equation, we get:
6 = L^2 - L
Rearranging the equation, we have:
L^2 - L - 6 = 0
Now we can factor this quadratic equation as:
(L - 3)(L + 2) = 0
Setting each factor equal to zero, we get two possible values for L:
L - 3 = 0 --> L = 3
L + 2 = 0 --> L = -2
Since the length cannot be negative, we discard L = -2. So, the length of the rectangle is L = 3 ft.
Now, we can find the width using Equation 1:
W = L - 1
W = 3 - 1
W = 2 ft
Therefore, the length of the rectangle is 3 ft and the width is 2 ft.