Respuesta :
Answer:
Option A - 342 feet
Step-by-step explanation:
Given : Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width.
To find : What is the perimeter of Janice fence if the area of her garden is 5,670 square feet?
Solution :
Let the width of the garden be w=x feet.
The garden has a length that is 9 feet less than 3 times its width.
The length of the garden be l=3x-9 feet
The area of the garden is A=5670 square feet.
The formula of area of garden is [tex]A=l\times w[/tex]
[tex]5670=(3x-9)\times x[/tex]
[tex]5670=3x^2-9x[/tex]
[tex]3x^2-9x-5670=0[/tex]
[tex]x^2-3x-1890=0[/tex]
[tex]x^2-45x+42x-1890=0[/tex]
[tex]x(x-45)+42(x-45)=0[/tex]
[tex](x-45)(x+42)=0[/tex]
[tex]x=45,-42[/tex]
Reject x=-42 as measurement cannot be negative.
The width of the garden is w=45 feet.
The length of the garden is l=3(45)-9=135-9=126 feet.
The perimeter of the garden is [tex]P=2(l+w)[/tex]
[tex]P=2(126+45)[/tex]
[tex]P=2(171)[/tex]
[tex]P=342[/tex]
The perimeter of Janice fence is 342 feet.
Therefore, Option A is correct.
