Answer:
the length of the quilt is 12 feet.
Explanation:
To find the length of Lisa's quilt, we can set up an equation using the given information. Let's say the length of the quilt is represented by 'x' feet.
According to the problem, the width of the quilt is 4 feet less than its length. So the width can be represented as (x - 4) feet.
The area of a rectangle is calculated by multiplying its length and width. Since the area of the quilt is given as 96 square feet, we can write the equation:
x * (x - 4) = 96
To solve this equation, we can first expand the equation:
x^2 - 4x = 96
Next, let's move all the terms to one side of the equation:
x^2 - 4x - 96 = 0
Now, we can factorize the quadratic equation:
(x - 12)(x + 8) = 0
Setting each factor equal to zero, we get:
x - 12 = 0 or x + 8 = 0
Solving for 'x' in each case, we find two possible solutions:
x = 12 or x = -8
Since the length of the quilt cannot be negative, we discard the solution x = -8.
Therefore, the length of the quilt is 12 feet.