Answer:
To find the dimensions of the rectangle, we can set up an equation based on the given information. Let's denote the width of the rectangle as "w" and the length as "l". According to the problem, the length is six feet less than its width, so we can express this relationship as:
l = w - 6
The area of a rectangle is given by the formula A = l * w. Substituting the expression for length from above, we have:
A = (w - 6) * w
Given that the area of the rectangle is 89 square feet, we can set up the equation:
89 = (w - 6) * w
Now, let's solve this quadratic equation to find the width of the rectangle. We can start by expanding the equation:
89 = w^2 - 6w
Rearranging the equation to bring all terms to one side:
w^2 - 6w - 89 = 0
To solve this quadratic equation, we can use factoring, completing the square, or applying the quadratic formula. In this case, let's use factoring. We need to find two numbers whose product is -89 and whose sum is -6. After some trial and error, we find that -11 and 8 satisfy these conditions:
(w - 11)(w + 8) = 0
Setting each factor equal to zero:
w - 11 = 0 or w + 8 = 0
Solving for "w" in each case:
w = 11 or w = -8
Since a negative width does not make sense in this context, we discard w = -8 as an extraneous solution.
Therefore, the width of the rectangle is w = 11 feet.
To find the length of the rectangle, we can substitute this value back into the expression for length:
l = w - 6
l = 11 - 6
l = 5 feet
So, the dimensions of the rectangle are a width of 11 feet and a length of 5 feet.
In summary, the dimensions of the rectangle with an area of 89 square feet, where the length is six feet less than its width, are a width of 11 feet and a length of 5 feet.
Explanation: