Select the correct answer.

Every morning, Jane runs around a rectangular garden with a length of [tex]$l$[/tex] and a width of [tex]$w$[/tex]. If she completes four laps around the garden, which expression best approximates the total distance she ran?

A. [tex][tex]$4(l+w)$[/tex][/tex]
B. [tex]$8(l+w)$[/tex]
C. [tex]$4(l)(w)$[/tex]
D. [tex][tex]$8(l)(w)$[/tex][/tex]



Answer :

To determine the correct answer, let's carefully break down the problem.

1. Understanding the Perimeter of a Rectangle:
The perimeter [tex]\(P\)[/tex] of a rectangular garden with length [tex]\(l\)[/tex] and width [tex]\(w\)[/tex] is calculated by the formula:
[tex]\[ P = 2(l + w) \][/tex]

2. Calculating the Total Distance Jane Runs in Four Laps:
Since the perimeter is the distance around the garden, if Jane completes one lap, she runs a distance equal to the perimeter.

If Jane completes four laps around the garden, the total distance [tex]\(D\)[/tex] she runs is:
[tex]\[ D = 4 \times P = 4 \times 2(l + w) = 8(l + w) \][/tex]

Therefore, the correct expression that approximates the total distance Jane ran after four laps is:
[tex]\[ \boxed{8(l+w)} \][/tex]

So, the correct answer is:

B. [tex]\(8(l+w)\)[/tex]