Given that the area of a rectangular patio is 105 ft².
The length of the patio is 8 ft longer than the width of the patio.
The equation is
[tex]w^2+8w-105=0[/tex][tex]We\text{ know that }8w=15w-7w\text{ and }15\times7=105.[/tex]The given equation can be written as follows.
[tex]w^2+15w-7w-105=0[/tex]Taking out the common terms.
[tex]w(w^{}+15)-7(w+15)=0[/tex][tex](w^{}+15)(w-7)=0[/tex][tex](w^{}+15)=0\text{ or }\mleft(w-7\mright)=0[/tex][tex]w=-15\text{ or }w=7[/tex]The measure can not be negative.
[tex]w=7\text{ ft.}[/tex]Hence the width of the patio is 7 ft.
Option D is correct.
