Mathematics
mattk
14

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

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(2) Answers
venkat

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

tuurajordan

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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