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A rectangular garden has a length that is modeled by the expression 2 x – 7 and a width of 3 x 2 + 4 x. Part A: What is the area of the garden? Part B: The owner of the garden wants to put a fence around the perimeter of the garden. Write an expression for the amount of fencing that the owner will need and solve to find the perimeter

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Answer:

Area(A) and perimeter(P) of rectangle  is given by:

[tex]A = lw[/tex]

[tex]P = 2(l+w)[/tex]

where,

l is the length and w is the width of the rectangle.

As per the statement:

A rectangular garden has a length that is modeled by the expression:

[tex]l = 2x-7[/tex] and a width(w) = [tex]3x^2+4x[/tex]

A.

To find the area of the garden.

then;

[tex]A = (2x-7)(3x^2+4x) = 6x^3+8x^2-21x^2-28x[/tex]

Combine like terms;

[tex]A = 6x^3-13x^2-28x[/tex] square units.

Therefore, the area of the garden is, [tex]6x^3-13x^2-28x[/tex] square units.

B.

The owner of the garden wants to put a fence around the perimeter of the garden.

then;

[tex]P = 2(2x-7+3x^2+4x) = 2(3x^2+6x-7)=6x^2+12x-14[/tex]

Therefore, the perimeter of the garden is, [tex]6x^2+12x-14[/tex] units

The area and perimeter of the rectangular garden are depended on its length and width which are given as 2x-7 and 3x^2 +4x.

Part A: The area of the garden is [tex]6x^3 -13x^2 -28x[/tex] square units.

Part B: The perimeter of the garden to put the fencing is [tex]6x^2 +12x -14[/tex] units.

What is the area and perimeter of the rectangle?

The area of a rectangle is the product of its length and width.

Area = Length [tex]\times[/tex] Width

The perimeter of a rectangle is the sum of all sides.

Perimeter = 2(Length + Width)

The length and width of the rectangular garden are given below.

[tex]l = 2x- 7[/tex]

[tex]w = 3 x^2+ 4 x[/tex]

Part A

The area of the garden is given below.

Area = Length [tex]\times[/tex] Width

[tex]A = (2x-7)(3x^2 + 4x)[/tex]

[tex]A = 6x^3 + 8x^2 -21x^2 - 28x[/tex]

[tex]A = 6x^3 -13x^2 -28x[/tex]

Hence the area of the garden is [tex]6x^3 -13x^2 -28x[/tex] square units.

Part B

The perimeter of the garden is given below.

Perimeter = 2 (length + width)

[tex]P = 2 (2x-7+ 3x^2 +4x)[/tex]

[tex]P = 2 ( 3x^2 +6x -7)[/tex]

[tex]P = 6x^2 +12x -14[/tex]

Hence the perimeter of the garden to put the fencing is [tex]6x^2 +12x -14[/tex] units.

To know more about the area and perimeter of the rectangle, follow the link given below.

https://brainly.com/question/1289811.

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