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A farmer's rectangular plot with a length of
l meters and a width of
w meters is shown in the figure. The perimeter, or distance around the plot, is 700 meters. Which of the following equations shows the perimeter of the plot in terms of length and width?
Choose 1 answer:
(A)
2l+2w=700
(B)
2l+2w=350
(c)
l+w=700
(D)
lw=700

A farmer's rectangular plot with a length of $l$ meters and a width of $w$ meters is shown in the figure. The perimeter, or distance around the plot, is $700$ meters. Which of the following equations shows the perimeter of the plot in terms of length and width? $\newline$ Choose $1$ answer: $\newline$ (A) $2 l+2 w=700$ $\newline$ (B) $2 l+2 w=350$ $\newline$ (C) $l+w=700$ $\newline$ (D) $l w=700$

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Solve a system of equations using any method: word problems

Full solution

Q. A farmer's rectangular plot with a length of

l

meters and a width of

w

meters is shown in the figure. The perimeter, or distance around the plot, is

700

meters. Which of the following equations shows the perimeter of the plot in terms of length and width?

\newline

Choose

1

answer:

\newline

(A)

2 l+2 w=700

\newline

(B)

2 l+2 w=350

\newline

(C)

l+w=700

\newline

(D)

l w=700

Question Prompt: The question prompt is: ＂What is the equation that represents the perimeter of the farmer's rectangular plot in terms of its length $l$ and width $w$ ?＂
Perimeter Formula: The perimeter of a rectangle is calculated by adding together twice the length and twice the width. The formula for the perimeter (P) of a rectangle is $P = 2l + 2w$ , where $l$ is the length and $w$ is the width.
Setting up the Equation: Given that the perimeter is $700$ meters, we can set up the equation using the formula for the perimeter of a rectangle: $2l + 2w = 700$ .
Checking Other Options: We can check the other options to ensure they do not represent the correct perimeter formula. Option (B) $2l + 2w = 350$ is incorrect because it would imply the perimeter is $350$ meters, not $700$ . Option (C) $l + w = 700$ is incorrect because it does not account for the fact that there are two lengths and two widths in the perimeter. Option (D) $lw = 700$ is incorrect because it represents the area of the rectangle, not the perimeter.

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