Question

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

Answer 1

Area: (2x - 7) * (3*2 + 4x)
          (2x - 7) * (6 + 4x)
                  8x-42

Perimeter: 2(2x - 7) + 2(3*2 + 4x)

Answer 2

Answer:

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

$A = lw$

$P = 2(l+w)$

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:

$l = 2x-7$ and a width(w) = $3x^2+4x$

A.

To find the area of the garden.

then;

$A = (2x-7)(3x^2+4x) = 6x^3+8x^2-21x^2-28x$

Combine like terms;

$A = 6x^3-13x^2-28x$ square units.

Therefore, the area of the garden is, $6x^3-13x^2-28x$ square units.

B.

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

then;

$P = 2(2x-7+3x^2+4x) = 2(3x^2+6x-7)=6x^2+12x-14$

Therefore, the perimeter of the garden is, $6x^2+12x-14$ units