Answer:
The dimensions of rectangle are:
Step-by-step explanation:
Let 'l' be the length and 'w' be the width of the rectangle
so
[tex]l=2w-3[/tex]
Also, the area of the rectangle is 27ft^2.
[tex]A=27\:ft^2[/tex]
As the area of the rectangle has the formula:
[tex]\:A\:=\:l\times w[/tex]
so
[tex]27=\:l\times w[/tex]
so the equation becomes
[tex]27=\left(2w-3\right)\times \:w[/tex]
[tex]27=2w^2-3w[/tex]
[tex]2w^2-3w-27=0[/tex]
[tex]\left(w+3\right)\left(2w-9\right)=0[/tex]
if [tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]w+3=0\quad \mathrm{or}\quad \:2w-9=0[/tex]
[tex]w=-3,\:w=\frac{9}{2}[/tex]
as the width can not be negative, so
[tex]w=\frac{9}{2}=4.5[/tex] ft
As
[tex]l=2w-3[/tex]
[tex]l=2\left(4.5\right)-3[/tex]
[tex]l=9-3[/tex]
[tex]l=6[/tex]
So the dimensions of rectangle are:
