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.
Hope this helped! :)
~Cam943, Junior Moderator
