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.

Step-by-step explanation:

Given

Dimension of photo frame is $20\ in.\times 24\ in.$

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 $x=2\ in.$