Questions: Solving and Modeling Two-Step Problems - Item 2456 Sanjay needs 90 meters of fence to surround a rectangular garden. The length of the garden is three times its width, w. Which of these equations give the correct formula for the perimeter? w+3 w=90 w+3 w+w+3 w=90 4 w=90 2 w+3 w=90

Solving and Modeling Two-Step Problems - Item 2456 Sanjay needs 90 meters of fence to surround a rectangular garden. The length of the garden is three times its width, w. Which of these equations give the correct formula for the perimeter? w+3 w=90 w+3 w+w+3 w=90 4 w=90 2 w+3 w=90
Transcript text: Solving and Modeling Two-Step Problems - Item 2456 Sanjay needs 90 meters of fence to surround a rectangular garden. The length of the garden is three times its width, $w$. Which of these equations give the correct formula for the perimeter? \[ w+3 w=90 \] \[ w+3 w+w+3 w=90 \] \[ 4 w=90 \] \[ 2 w+3 w=90 \]
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Solution

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Solution Steps

Step 1: Express the length in terms of width

The length of the garden is three times its width, \(w\). So, length \(l = 3w\).

Step 2: Write the formula for the perimeter

The perimeter of a rectangle is given by \(P = 2(l+w)\). We are given that the perimeter is 90 meters. So, \(90 = 2(l+w)\).

Step 3: Substitute the length in terms of width

Substitute \(l = 3w\) into the perimeter formula: \(90 = 2(3w + w)\) \(90 = 2(4w)\) \(90 = 8w\)

Alternatively, \(90 = 2(3w + w)\) \(90 = 2(3w) + 2(w)\) \(90 = 6w + 2w\) \(90 = w + 3w + w + 3w\)

Final Answer

\(w+3w+w+3w=90\)

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