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

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

Answer 2

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= (-b± √(b^2-4ac) )/(2a)`

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


`( √(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