Question

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 1

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. 

Hope this helped! :) 

~Cam943, Junior Moderator

Answer 2

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