The width of a rectangle is 1 ft. less than the length. The area is 12ft.^2. Find the length and width.

length = x

width = x-l

area = length*width
12 = (x)*(x-1)
solve for x...
use the equations above to get the length and width..

To find the length and width of the rectangle, we can use the given information about the relationship between the width and the length, as well as the area.

Let's represent 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. Therefore, we can write an equation based on this information:

W = L - 1 (Equation 1)

The formula for the area of a rectangle is: A = L * W

Given that the area is 12 ft^2, we can substitute the values into the equation:

12 = L * W

Since we know that W = L - 1, we can substitute this expression into the equation:

12 = L * (L - 1)

Expanding this equation, we have:

12 = L^2 - L

Rearranging the terms, we get:

L^2 - L - 12 = 0

Now, we have a quadratic equation. To solve it, we can factorize or use the quadratic formula. In this case, let's factorize:

(L - 4) * (L + 3) = 0

This gives us two possible solutions for L:

L - 4 = 0 (L = 4)

L + 3 = 0 (L = -3)

Since we cannot have a negative length for our rectangle, we discard the negative value.

Hence, the length of the rectangle is L = 4 ft.

To find the width, we substitute the value of L into Equation 1:

W = L - 1
W = 4 - 1
W = 3 ft.

So, the length of the rectangle is 4 ft, and the width is 3 ft.