Answer:
The dimensions of the porch are [tex]25\ ft[/tex] by [tex]20\ ft[/tex]
Step-by-step explanation:
we know that
The area of the porch is equal to the length multiplied by the width
[tex]A=(2x+3)(x+9)[/tex]
[tex]A=500\ ft^{2}[/tex]
so
[tex]500=(2x+3)(x+9)[/tex]
Solve for x
[tex]500=2x^{2} +18x+3x+27\\ \\2x^{2} +21x-473=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]x=11\ ft[/tex]
see the attached figure
The dimensions are
[tex](2x+3)=2(11)+3=25\ ft[/tex]
[tex](x+9)=11+9=20\ ft[/tex]
