Question

Josephine has a rectangular garden with an area of 2x2 + x – 6 square feet. Which expressions can represent the length and width of the garden? Length = x2 – 3 feet; width = 2 feet length = 2x + 3 feet; width = x – 2 feet length = 2x + 2 feet; width = x – 3 feet length = 2x – 3 feet; width = x + 2 feet

Answer 1

Answer: The answer is d

Explanation:

Answer 2

feet length = 2x – 3 feet; width = x + 2 feet

Explanation:

we have

The area of a rectangular garden in square feet is

`A=2x^(2)+x-6`

Remember that

The area of a rectangular garden is

`A=LW`

where

L is the length and W is the width

Convert the equation in factored form

`2x^(2)+x-6=0`

`2x^(2)+x=6`

Factor the leading coefficient

`2(x^(2)+0.5x)=6`

Complete the square

`2(x^(2)+0.5x+1/16)=6+1/8`

`2(x^(2)+0.5x+1/16)=49/8`

Rewrite as perfect square

`2(x+1/4)^(2)=49/8`

`(x+1/4)^(2)=49/16`

square root both sides

`(x+1/4)=(+/-)(7/4)`

`x=-1/4(+/-)(7/4)`

`x=-1/4(+)(7/4)=3/2`

`x=-1/4(-)(7/4)=-2`

so

`2x^(2)+x-6=(x-3/2)(x+2)`

`2x^(2)+x-6=(2x-3)(x+2)`

therefore

feet length = 2x – 3 feet; width = x + 2 feet