Final answer:
To find the width and height of the door, set up two equations based on the given information. Solve the quadratic equation to find the dimensions.
Step-by-step explanation:
To find the width and height of the door, we can set up two equations based on the given information. Let's say the width of the door is x. According to the problem, the height of the door is 2.4 feet longer than its width, so the height would be x + 2.4.
We know that the front area of the door is 1527.4 square feet, which can be represented by the equation x * (x + 2.4) = 1527.4.
By solving this quadratic equation, we can find the width (x) and height (x + 2.4) of the door.