Question

the frame of a picture is 28 cm by 32 cm outside and is of uniform width.What is the width of the frame if 192 cm2 of the picture shows

Answer 1

Answer:

The width of the frame is equal to $8\ cm$  

Step-by-step explanation:

Let

x-------> the width of the frame picture

we know that

$(28-2x)(32-2x)=192$    

$896-56x-64x+4x^{2} =192$

$4x^{2}-120x+704=0$  

Simplify

$x^{2}-30x+176=0$

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

$x^{2}-30x+176=0$

so

$a=1\\b=-30\\c=176$

substitute in the formula

$x=\frac{30(+/-)\sqrt{(-30)^{2}-4(1)(176)}} {2(1)}$

$x=\frac{30(+/-)\sqrt{196}} {2}$

$x=\frac{30(+/-)14} {2}$

$x=\frac{30+14} {2}=22\ cm$  ----> this solution is not logic

$x=\frac{30-14} {2}=8\ cm$  

The width of the frame is equal to $8\ cm$