Question

Question 25 Janice puts a fence around her rectangular garden. The garden has a length that is 9 feet less than 3 times its width. What is the perimeter of Janice’s fence if the area of her garden is 5,670 square feet?

A) 342 feet
B) 318 feet
C) 300 feet
D) 270 feet

Answer 1

Option A - 342 feet

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
`A=l* w`

`5670=(3x-9)* x`

`5670=3x^2-9x`

`3x^2-9x-5670=0`

`x^2-3x-1890=0`

`x^2-45x+42x-1890=0`

`x(x-45)+42(x-45)=0`

`(x-45)(x+42)=0`

`x=45,-42`

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
`P=2(l+w)`

`P=2(126+45)`

`P=2(171)`

`P=342`

The perimeter of Janice fence is 342 feet.

Therefore, Option A is correct.