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 width ≥10 for all options

• Option 1: $w=5$, $5<10$ → invalid
• Option 2: $w=10$, $10≥10$ → valid so far
• Option 3: $w=20$, $20≥10$ → valid so far
• Option 4: $w=30$, $30≥10$ → valid so far

Step2: Check $2l+2w ≤150$ for remaining options

For Option 2:

$2(20)+2(10)=40+20=60$
$60 ≤150$ → valid

For Option 3:

$2(60)+2(20)=120+40=160$
$160>150$ → invalid

For Option 4:

$2(55)+2(30)=110+60=170$
$170>150$ → invalid

Answer:

$l=20$ ft; $w=10$ ft