We know that the formula for the area of a rectangle is:

\( A=lw \)

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

Let the width of the rectangle be "\( x \)"

Then the length of the rectangle is \( 3x+2 \)

Substitute.

\( (3x+2)(x)=156 \)

Multiply the terms.

\( 3x^2+2x=156 \)

Bring the 156 over.

\( 3x^2+2x-156=0 \)

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

\( x= \frac{-b± \sqrt{b^2-4ac} }{2a} \)

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

\( \frac{ \sqrt{469}-1 }{3} \)

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

L×b=area

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