The length of a rectangular mural is 2ft. more than three times the width the area is 165 sq. ft. Find the Width And Length

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


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