Answer:
The width of the border is [tex]1.5\ in[/tex]
Step-by-step explanation:
Let
x-----> the width of the border
we know that
The area of the photo is equal to
[tex](11-2x)(13-2x)=80\\ 143-22x-26x+4x^{2}=80\\4x^{2}-48x+63=0[/tex]
solve the quadratic equation
The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]4x^{2}-48x+63=0[/tex]
so
[tex]a=4\\b=-48\\c=63[/tex]
substitute in the formula
[tex]x=\frac{48(+/-)\sqrt{-48^{2}-4(4)(63)}} {2(4)}[/tex]
[tex]x=\frac{48(+/-)\sqrt{1,296}} {8}[/tex]
[tex]x=\frac{48(+/-)36 {8}[/tex]
[tex]x=\frac{48(+)36 {8}=10.5\ in[/tex] -----> not make sense
[tex]x=\frac{48(-)36 {8}=1.5\ in[/tex] -----> solution
