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

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

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(+/-)√(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`