## Answer :

[tex]A=lw[/tex]

We know that the area is 165. Now we need to solve for the dimensions.

Let the width of the rectangle be "[tex]x[/tex]"

Then the length of the rectangle is [tex]3x+2[/tex]

Substitute.

[tex](3x+2)(x)=156[/tex]

Multiply the terms.

[tex]3x^2+2x=156[/tex]

Bring the 156 over.

[tex]3x^2+2x-156=0[/tex]

We have to use the quadratic formula to solve this now. Let us restate it:

[tex]x= \frac{-b± \sqrt{b^2-4ac} }{2a} [/tex]

Now I'm going to fast forward this because all the rest is boring stuff and substitution. The answer is:

[tex] \frac{ \sqrt{469}-1 }{3} [/tex]

Since we cannot have a negative answer, we must cancel out the other answer, which I did not include.

Hope this helped! :)

~Cam943, Junior Moderator

l=2+3b

2+3b ×b=165

3b²=163

b²=54.3

b=√54.3

b=7.37 or 7.4=7

b=7ft

l=2+3(7.4)

l=2+ 22.2

l=24.2=24

l=24ft