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?

Question

asked Aug 16, 2021 161k views

1 Answer

Yucel Bayram · Answer 1 · 2021-08-20T18:14:08+0000

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
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
$x=2\ in.$