Question

irina 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? (\bigcirc) ( l = 20 ) ft; ( w = 5 ) ft (\bigcirc) ( l = 20 ) ft; ( w = 10 ) ft (\bigcirc) ( l = 60 ) ft; ( w = 20 ) ft (\bigcirc) ( l = 55 ) ft; ( w = 30 ) ft

Explanation:

Step1: Check \( w \geq 10 \) for each option

• Option 1: \( w = 5 \) ft. \( 5 \geq 10 \) is false. Eliminate.
• Option 2: \( w = 10 \) ft. \( 10 \geq 10 \) is true. Proceed.
• Option 3: \( w = 20 \) ft. \( 20 \geq 10 \) is true. Proceed.
• Option 4: \( w = 30 \) ft. \( 30 \geq 10 \) is true. Proceed.

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

• Option 2: \( l = 20 \), \( w = 10 \). \( 2(20) + 2(10) = 40 + 20 = 60 \). \( 60 \leq 150 \) is true.
• Option 3: \( l = 60 \), \( w = 20 \). \( 2(60) + 2(20) = 120 + 40 = 160 \). \( 160 \leq 150 \) is false. Eliminate.
• Option 4: \( l = 55 \), \( w = 30 \). \( 2(55) + 2(30) = 110 + 60 = 170 \). \( 170 \leq 150 \) is false. Eliminate.

Answer:

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