The rectangle shown has an area of 27 cm2 and is modeled by the equation A = 2w2 + 3w, where w is the width. What is the length of the rectangle?

Answer:The length of the rectangle is [tex]9\ cm[/tex] Step-by-step explanation:we know thatThe area of rectangle is equal to[tex]A=LW[/tex]In this problem we have[tex]A=27\ cm^{2}[/tex]so[tex]27=LW[/tex] ------> equation Aand[tex]A=2w^{2}+3w[/tex]so[tex]27=2w^{2}+3w[/tex][tex]2w^{2}+3w-27=0[/tex]The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex] in this problem we have [tex]2w^{2}+3w-27=0[/tex]so [tex]a=2\\b=3\\c=-27[/tex] substitute in the formula [tex]w=\frac{-3(+/-)\sqrt{3^{2}-4(2)(-27)}} {2(2)}[/tex] [tex]w=\frac{-3(+/-)\sqrt{225}} {4}[/tex] [tex]w=\frac{-3(+/-)15} {4}[/tex] [tex]w=\frac{-3(+)15} {4}=3[/tex] [tex]w=\frac{-3(-)15} {4}=-4.5[/tex] The solution of the quadratic equation is[tex]w= 3\ cm[/tex]Find the value of L[tex]27=L(3)[/tex] [tex]L=27/3=9\ cm[/tex]