Answer:
[tex]Length=27feet\\Width=12 feet[/tex]
Step-by-step explanation:
Let, the length of the rectangle be 'L'
and, width of the rectangle be 'W'
length=2*Width+3
[tex]L=(2W+3) feet\\\\[/tex]
Area of the rectangle= 90 square feet
Area of a rectangle = Length*Width
[tex]90=(2W+3)*W\\\\2W^2+3W=90\\\\2W^2+3W-90=0\\\\[/tex]
Using Factorization Method to solve quadratic equation:
[tex]2W^2-12W+15W-90=0[/tex]
Taking common from the equation:
[tex]2W(W-12)+15(W-12)=90\\\\(W-12)(2W+15)=0\\\\W-12=0\\\\W=12 feet[/tex]
OR
[tex]2W+15=0\\\\2W=-15\\\\W=-7.5 feet[/tex]
The Width cannot be negative, therefore Width(W)=12 feet
[tex]Length=2*Width+3\\\\=(12*2)+3\\\\=24+3\\\\=27 feet[/tex]
[tex]Length=27feet\\Width=12 feet[/tex]
