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reinhard10158

Step-by-step explanation:

20 ft of fencing means that this is the perimeter of the pen.

the perimeter of a rectangle is

2×length + 2×width = 20

we can simplify this by dividing both sides by 2 :

length + width = 10

length = 10 - width

the area of a rectangle is

length×width

and when we use the first equation now in this second, we get as area

(10 - width) × width = 10×width - width²

so, this is a quadratic expression.

if 2 ft of fencing are damaged, then he has only 18 ft available.

so, the perimeter is

2×length + 2×width = 18

or then

length + width = 9

length = 9 - width

and the expression for the area is

length×width = (9 - width) × width = 9×width - width²

of course, the area is smaller.

The quadratic expression for the required area is 9b - b² here b is the width of the pen.

What is the perimeter of the rectangle?

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle  and L is the length of the rectangle

The perimeter of the pen is indicated by the 20 feet of fencing.

Let b is the width of the rectangle and a be the length of rectangle

The perimeter of a rectangle = 2(L+W)

⇒ 2(a + b) = 20

Divided by 2 both sides

⇒ a + b = 10

⇒ a = 10 - b

Since the area of a rectangle is length × width

and we obtain an area when we apply the first equation to the second one right now.

⇒ (10 - b) × width

⇒ 10b- b²

So, this is a quadratic expression.

He only has 18 feet available if 2 feet of the fencing are damaged.

So, the perimeter is

⇒ 2a + 2b = 18

⇒ a + b= 9

⇒ a = 9 - b

Now, the expression for the required area is

⇒ a × b

⇒ (9 - b) × b

⇒  9b - b²

Hence, the quadratic expression for the required area is 9b - b².

Learn more about the Perimeter of the rectangle here:

brainly.com/question/15287805

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