Question

A photo is printed on a 20-inch by 24-inch piece of paper. The photo covers 320 square inches and has a ubiform border. What is the width of

the border?

Answer 1

Answer:2 in.

Explanation:

Given

Dimension of photo frame is
`20\ in.* 24\ in.`

If the photo cover an area of
`320\ in.^2`

Suppose x be the width of border

Therefore dimension of frame without border is

`A'=(20-2x)(24-2x)`

And
`A'` must be equal to
`320\ in.^2`

So,

`\Rightarrow (20-2x)(24-2x)=320`

`\Rightarrow (10-x)(12-x)=80`

`\Rightarrow 120-10x-12x+x^2=80`

`\Rightarrow x^2-22x+40=0`

`\Rightarrow x^2-20x-2x+40=0`

`\Rightarrow (x-2)(x-20)=0`

Thus there are two values of x out of which
`x=20\ in.` is not valid because it is not feasible

thus width of border is
`x=2\ in.`