Answer: The width is [tex]x^{2}[/tex] + 1x -4
Step-by-step explanation:
We know to find the perimeter we have to add the distance around the rectangle.The distance can also be sought as 2 times the length plus times the width.
So as a formula is like P = 2l + 2w where P is the perimeter.
We are given the perimeter so we can plot it into the formula and also plot in the length because it says the length is 3x -1
[tex]2x^{2}[/tex]+8x - 10 = 2(3x -1) + 2w Now we have to solve for w .Break it down
([tex]2x^{2}[/tex] + 8x -10) = (6x -2 )+ 2w subtract 6x - 2 from both sides
([tex]2x^{2}[/tex] + 8x -10) - (6x -2) = 2w
( [tex]2x^{2}[/tex] + 2x -8) = 2w now divide both sides by 2
[tex]\frac{2x^{2} +2x-8 }{2} = w[/tex] One the left side factor the numerator
[tex]\frac{2(x^{2} +1x-4)}{2}[/tex] = w Now multiply both sides by 2
w =( [tex]x^{2}[/tex] + 1x-4 )
The width is x^2 + 1x -4
