Question

select the correct answer.
every morning, jane runs around a rectangular garden with a length of l and a width of w. if she completes four laps around the garden, which expression best approximates the total distance she ran?
a. 4(l + w)
b. 8(l + w)
c. 4(l)(w)
d. 8(l)(w)

Explanation:

Step1: Find perimeter of rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \), where \( l \) is length and \( w \) is width.

Step2: Calculate total distance for 4 laps

For 4 laps, total distance \( D = 4\times P = 4\times2(l + w)=8(l + w) \)? Wait, no, wait. Wait, perimeter is \( 2(l + w) \), so one lap is \( 2(l + w) \), four laps would be \( 4\times2(l + w) \)? Wait, no, wait, no, I made a mistake. Wait, perimeter of rectangle is \( 2(l + w) \), so one lap is \( 2(l + w) \), four laps: \( 4\times2(l + w) = 8(l + w) \)? Wait, no, wait the options: option B is \( 8(l + w) \), option A is \( 4(l + w) \). Wait, no, wait, let's re - calculate.

Wait, perimeter of a rectangle: \( P=2(l + w) \). So one lap is \( 2(l + w) \). Four laps: \( 4\times P=4\times2(l + w) = 8(l + w) \)? Wait, but let's check the options again. Wait, maybe I messed up. Wait, no, wait the formula for the perimeter of a rectangle is \( P = 2\times(\text{length}+\text{width})=2(l + w) \). So if Jane runs 4 laps, the total distance \( d = 4\times P=4\times2(l + w)=8(l + w) \). Wait, but let's check the options. Option B is \( 8(l + w) \), option A is \( 4(l + w) \). Wait, maybe I made a mistake in the perimeter formula? No, perimeter of a rectangle is \( 2(l + w) \). So one lap is \( 2(l + w) \), four laps: \( 4\times2(l + w)=8(l + w) \). So the correct expression is \( 8(l + w) \), which is option B.

Wait, no, wait, wait, I think I made a mistake. Wait, let's re - do:

Perimeter of rectangle: \( P = 2(l + w) \).

Distance for 1 lap: \( 2(l + w) \).

Distance for 4 laps: \( 4\times2(l + w)=8(l + w) \). So the answer should be option B.

Answer:

B. \( 8(l + w) \)