<u>Given</u>:
The length of a rectangle is 5 less than its width.
The area of the rectangle is 84 square feet.
We need to determine the quadratic equation in standard form that represents the area of the rectangle.
<u>Dimensions of the rectangle:</u>
Let l denote the length of the rectangle.
Let w denote the width of the rectangle.
Since, it is given that the length is 5 less than its width, it can be written as,
and
<u>Area of the rectangle:</u>
The area of the rectangle can be determined using the formula,
Substituting A = 84, and
, we get
Adding both sides of the equation by w², we have;
Subtracting by 5w on both sides, we get;
Thus, the quadratic equation in standard form for the area of the rectangle is