A rectangular garden has a length of 60 feet ( ft ), a width of wft, and a perimeter of 200ft. Which of the following equations best models the garden's perimeter? Choose 1 answer: (A) 60+w=200 (B) 60+2w=200 (C) 120+w=200 (D) 120+2w=200

Recall Perimeter Formula: To find the equation that models the perimeter of the rectangular garden, we need to recall the formula for the perimeter of a rectangle, which is P = 2l + 2w, where P is the perimeter, l is the length, and w is the width.Substitute Given Values: We are given the length l = 60 feet, the width w feet (unknown), and the perimeter P = 200 feet. We can substitute these values into the perimeter formula to find the equation that represents the perimeter of the garden.Simplify Equation: Substituting the given values into the perimeter formula, we get: 200 = 2(60) + 2wCheck Answer Choices: Simplify the equation by multiplying 2 with 60, which gives us: 200 = 120 + 2wThe equation 200 = 120 + 2w matches one of the answer choices provided. We can now check the answer choices to see which one corresponds to our equation.Comparing our equation with the answer choices, we find that: (A) 60 + w = 200 (Incorrect, does not account for both pairs of sides) (B) 60 + 2w = 200 (Incorrect, does not account for both pairs of sides) (C) 120 + w = 200 (Incorrect, does not account for the multiplication by 2 for the width) (D) 120 + 2w = 200 (Correct, matches our equation)

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A rectangular garden has a length of 60 feet (
ft ), a width of
wft, and a perimeter of
200ft. Which of the following equations best models the garden's perimeter?
Choose 1 answer:
(A)
60+w=200
(B)
60+2w=200
(C)
120+w=200
(D)
120+2w=200

A rectangular garden has a length of $60$ feet ( $\mathrm{ft}$ ), a width of $w$ $\mathrm{ft}$ , and a perimeter of $200$ $\mathrm{ft}$ . Which of the following equations best models the garden's perimeter? $\newline$ Choose $1$ answer: $\newline$ (A) $60+w=200$ $\newline$ (B) $60+2 w=200$ $\newline$ (C) $120+w=200$ $\newline$ (D) $120+2 w=200$

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Math Problems

Algebra 1

Solve a system of equations using substitution: word problems

Full solution

Q. A rectangular garden has a length of

60

feet (

\mathrm{ft}

), a width of

w

\mathrm{ft}

, and a perimeter of

200

\mathrm{ft}

. Which of the following equations best models the garden's perimeter?

\newline

Choose

1

answer:

\newline

(A)

60+w=200

\newline

(B)

60+2 w=200

\newline

(C)

120+w=200

\newline

(D)

120+2 w=200

Recall Perimeter Formula: To find the equation that models the perimeter of the rectangular garden, we need to recall the formula for the perimeter of a rectangle, which is $P = 2l + 2w$ , where $P$ is the perimeter, $l$ is the length, and $w$ is the width.
Substitute Given Values: We are given the length $l = 60$ feet, the width $w$ feet (unknown), and the perimeter $P = 200$ feet. We can substitute these values into the perimeter formula to find the equation that represents the perimeter of the garden.
Simplify Equation: Substituting the given values into the perimeter formula, we get: $200 = 2(60) + 2w$
Check Answer Choices: Simplify the equation by multiplying $2$ with $60$ , which gives us: $200 = 120 + 2w$
Check Answer Choices: Simplify the equation by multiplying $2$ with $60$ , which gives us: $\newline$ $200 = 120 + 2w$ The equation $200 = 120 + 2w$ matches one of the answer choices provided. We can now check the answer choices to see which one corresponds to our equation.
Check Answer Choices: Simplify the equation by multiplying $2$ with $60$ , which gives us: $200 = 120 + 2w$ The equation $200 = 120 + 2w$ matches one of the answer choices provided. We can now check the answer choices to see which one corresponds to our equation. Comparing our equation with the answer choices, we find that: (A) $60 + w = 200$ (Incorrect, does not account for both pairs of sides) (B) $60 + 2w = 200$ (Incorrect, does not account for both pairs of sides) (C) $120 + w = 200$ (Incorrect, does not account for the multiplication by $2$ for the width) (D) $120 + 2w = 200$ (Correct, matches our equation)