Answer:
The ratio of the area to the width is equal to [tex](x+4)\ units[/tex]
Step-by-step explanation:
we know that
[tex]A=x^{2} +3x-4[/tex]
Completing the square
[tex]x^{2} +3x=4[/tex]
[tex](x^{2} +3x+(9/4))=4+(9/4)[/tex]
[tex](x^{2} +3x+(9/4))=25/4[/tex]
[tex](x+(3/2))^{2}=25/4[/tex]
[tex](x+(3/2))=(+/-)5/2[/tex]
[tex]x=-(3/2)(+/-)5/2[/tex]
[tex]x=-(3/2)(+)5/2=1[/tex]
[tex]x=-(3/2)(-)5/2=-4[/tex]
therefore
[tex]x^{2} +3x-4=(x-1)(x+4)[/tex]
Find the ratio of the area to the width
[tex]\frac{A}{W}=\frac{(x-1)(x+4)}{x-1}=(x+4)\ units[/tex]
