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

Answer :

Cam943
We know that the formula for the area of a rectangle is: 

[tex]A=lw[/tex] 

We know that the area is 165. Now we need to solve for the dimensions. 

Let the width of the rectangle be "[tex]x[/tex]"

Then the length of the rectangle is [tex]3x+2[/tex] 

Substitute. 

[tex](3x+2)(x)=156[/tex] 

Multiply the terms. 

[tex]3x^2+2x=156[/tex] 

Bring the 156 over. 

[tex]3x^2+2x-156=0[/tex] 

We have to use the quadratic formula to solve this now. Let us restate it: 

[tex]x= \frac{-b± \sqrt{b^2-4ac} }{2a} [/tex]

Now I'm going to fast forward this because all the rest is boring stuff and substitution. The answer is: 

[tex] \frac{ \sqrt{469}-1 }{3} [/tex]

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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