# 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: [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