Question

jackson likes to go running around the perimeters of two fields near his home. the two fields have side dimensions as shown in the diagrams.
if the perimeter of rectangle a is $f(x)$ and the perimeter of rectangle b is $g(x)$, which function represents the difference, $h(x)$, in the perimeters of the rectangles?
$h(x)=0.5x^{2}-3x$
$h(x)=-x+2$
$h(x)=x+6$
$h(x)=-x-6$
rectangle a: side lengths $x-1$ and $2x$
rectangle b: side lengths $0.5x$ and $3x+2$

Explanation:

Step1: Calculate perimeter of A

Perimeter of rectangle: $P=2(l+w)$. For A, $l=2x$, $w=x-1$.
$$f(x)=2(2x + x - 1)=2(3x - 1)=6x - 2$$

Step2: Calculate perimeter of B

For B, $l=3x+2$, $w=0.5x$.
$$g(x)=2(3x + 2 + 0.5x)=2(3.5x + 2)=7x + 4$$

Step3: Find difference $h(x)=f(x)-g(x)$

Substitute the two functions:
$$h(x)=(6x - 2)-(7x + 4)=6x - 2 -7x -4=-x -6$$

Answer:

$h(x)=-x -6$ (the fourth option)