Question

shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster. the area of the enlarged photo is 256 square inches. in the equation (x 10)2 = 256, x represents the side measure of the original square photo. what were the dimensions of the original photo? 4 inches by 4 inches 6 inches by 6 inches 10 inches by 10 inches 12 inches by 12 inches

Answer 1

Hello,

Answer B 6*6 in²

(x+10)²=256
==>(x+10)²-16²=0
==>(x+10-16)(x+10+16)=0
==>x=6 or x=-26 (excluded)

Answer 2

The original dimension was 6 inches by 6 inches.

Explanation:

'x' represents the side measure of the original square photo.

Given is that Shayna enlarged a square photo by adding 10 inches to each side so it could be seen on a large poster.

The given equation is:

`(x+10)^(2) =256`

Solving for 'x' as x was the original dimension in which 10 was added.

`x^(2) +20x+100=256`

`x^(2) +20x-156=0`

`x^(2) +26x-6x-156=0`

`x(x+26)-6(x+26)=0`

`(x+26)(x-6)=0`

`x=-26` and
`x=6`

Neglecting the negative value as dimension cannot be negative.

So, we have x=6 inch

Therefore, the original dimension was 6 inches by 6 inches.