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

factor
2x^2+x-6
trial and error, the factors are the legnth and width
or, we could try multiplying the given options
if we do we find the factored form is
(x+2)(2x-3)
answer is last one

Answer Link

calculista calculista · Answer 2 · 2018-11-04T16:02:15-05:00

we have

\(2x^{2} +x-6\)

we know that

The area of a rectangle is equal to

\(A=L*W\)

where

L is the length side of the rectangle

W is the width side of the rectangle

In this problem

Equate the area to zero and Find the roots of the quadratic equation

\(2x^{2} +x-6=0\)

Group terms that contain the same variable, and move the constant to the opposite side of the equation

\(2x^{2} +x=6\)

Factor the leading coefficient

\(2(x^{2} +0.5x)=6\)

Complete the square. Remember to balance the equation by adding the same constants to each side

\(2(x^{2} +0.5x+0.25^{2})=6+0.125\)

\(2(x^{2} +0.5x+0.0625=6.125\)

Rewrite as perfect squares

\(2(x+0.25)^{2}=6.125\)

\((x+0.25)^{2}=3.0625\)

Square root both sides

\((x+0.25)=(+/-)\sqrt{3.0625}\)

\((x+0.25)=(+/-)1.75\)

\(x1=-0.25+1.75=1.50\)

\(x2=-0.25-1.75=-2\)

so

\(2x^{2} +x-6=2(x+2)(x-1.50)\)

\(2(x+2)(x-1.50)=(x+2)(2x-3)\)

\(length=(2x-3)\ feet\)

\(width=(x+2)\ feet\)

therefore

the answer is the option

\(length=(2x-3)\ feet\) ; \(width=(x+2)\ feet\)