Question

inna wants to build a fence around a rectangular vegetable garden so that it has a width of at least 10 feet. she can use a maximum of 150 feet of fencing. the system of inequalities that models the possible lengths, l, and widths, w, of her garden is shown.
$w \geq 10$
$2l + 2w \leq 150$
which length and width are possible dimensions for the garden?
\\( l = 20 \\) ft; \\( w = 5 \\) ft
\\( l = 20 \\) ft; \\( w = 10 \\) ft
\\( l = 60 \\) ft; \\( w = 20 \\) ft
\\( l = 55 \\) ft; \\( w = 30 \\) ft

Explanation:

Step1: Check \( w \geq 10 \)

For each option, verify if width \( w \geq 10 \).

• Option 1: \( w = 5 \), \( 5 < 10 \) → Reject.
• Option 2: \( w = 10 \), \( 10 \geq 10 \) → Keep.
• Option 3: \( w = 20 \), \( 20 \geq 10 \) → Keep.
• Option 4: \( w = 30 \), \( 30 \geq 10 \) → Keep.

Step2: Check \( 2l + 2w \leq 150 \)

Simplify to \( l + w \leq 75 \) (divide by 2).

• Option 2: \( l = 20 \), \( w = 10 \). \( 20 + 10 = 30 \leq 75 \) → Keep.
• Option 3: \( l = 60 \), \( w = 20 \). \( 60 + 20 = 80 > 75 \) → Reject.
• Option 4: \( l = 55 \), \( w = 30 \). \( 55 + 30 = 85 > 75 \) → Reject.

Answer:

B. \( l = 20 \) ft; \( w = 10 \) ft