Answer:
12.244 cm long
Explanation:
The area of a rectangle is equal to its height times its width, so if the piece of cardboard has an area of 66 square centimeters and is 5 centimeters longer than it is tall, we can write the following equation to represent the dimensions of the piece of cardboard:
height * (height + 5) = 66
To solve this equation, we can first divide both sides of the equation by the height of the piece of cardboard to get:
height + 5 = 66 / height
We can then subtract 5 from both sides of the equation to get:
height = 66 / height - 5
We can then multiply both sides of the equation by the height to get:
height^2 = 66 - 5 * height
We can then use the quadratic formula to solve for the height of the piece of cardboard:
height = (-5 +/- sqrt(5^2 - 4 * 1 * -66)) / (2 * 1)
The value of the square root in the quadratic formula must be positive, so we take the positive value for the height:
height = (-5 + sqrt(5^2 + 4 * 1 * 66)) / (2 * 1)
This simplifies to:
height = (5 + sqrt(61)) / 2
The height of the piece of cardboard is approximately 7.244 centimeters. Since the piece of cardboard is 5 centimeters longer than it is tall, it must be 5 + 7.244 = 12.244 centimeters long.
Therefore, the piece of cardboard is approximately 12.244 centimeters long.