A photo is printed on an 11-inch by 13-inch piece of paper. The photo covers 80 square inches and has a uniform border. What is the width of the border? Don't use a graph t…

Question

asked May 9, 2020 227k views

1 Answer

Zeliax · Answer 1 · 2020-05-15T09:43:26+0000

Answer:

The width of the border is
$1.5\ in$

Explanation:

Let

x-----> the width of the border

we know that

The area of the photo is equal to

$(11-2x)(13-2x)=80\\ 143-22x-26x+4x^(2)=80\\4x^(2)-48x+63=0$

solve the quadratic equation

The formula to solve a quadratic equation of the form
ax^(2) +bx+c=0 is equal to

$x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}$

in this problem we have

4x^(2)-48x+63=0

so

$a=4\\b=-48\\c=63$

substitute in the formula

$x=\frac{48(+/-)\sqrt{-48^(2)-4(4)(63)}} {2(4)}$

$x=\frac{48(+/-)√(1,296)} {8}$

$x=\frac{48(+/-)36 {8}$

$x=\frac{48(+)36 {8}=10.5\ in$ -----> not make sense

$x=\frac{48(-)36 {8}=1.5\ in$ -----> solution