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

(2) Answers

We know that the formula for the area of a rectangle is:  [latex]A=lw[/latex]  We know that the area is 165. Now we need to solve for the dimensions.  Let the width of the rectangle be "[latex]x[/latex]" Then the length of the rectangle is [latex]3x+2[/latex]  Substitute.  [latex](3x+2)(x)=156[/latex]  Multiply the terms.  [latex]3x^2+2x=156[/latex]  Bring the 156 over.  [latex]3x^2+2x-156=0[/latex]  We have to use the quadratic formula to solve this now. Let us restate it:  [latex]x= \frac{-b± \sqrt{b^2-4ac} }{2a} [/latex] Now I'm going to fast forward this because all the rest is boring stuff and substitution. The answer is:  [latex] \frac{ \sqrt{469}-1 }{3} [/latex] 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×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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