The equation which represent the area of rectangle is [tex]2w^{2} +3w=90[/tex] and the width of the rectangle is 6 inches.
The area is the amount of space within the perimeter of a 2D shape.
area of rectangle = length × width
According to the given question
we have
width of the rectangle is w
length of the rectangle = 3+2w
area of rectangle = 90 square inches.
Therefore,
An equation that represents the area
area of rectangle = length × width
⇒ 90 = (3+2w)×w
⇒ 90 = [tex]3w+2w^{2}[/tex]
or [tex]2w^{2}+3w=90[/tex] represents the equation for area.
For width,
solve the above equation
[tex]2w^{2} +3w-90=0[/tex]
[tex]2w^{2}+15w-12w-90=0[/tex]
[tex]2w^{2} -12w+15w-90=0[/tex]
[tex]2w(w-6)+15(w-6)=0[/tex]
[tex](2w+15)(w-6)=0[/tex]
[tex]w=6,\frac{-15}{2}[/tex]
Hence, the width of rectangle is 6inches.
( [tex]\frac{-15}{2}[/tex] is not possible because with will never be negative)
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