Question

The combined area of the photo and mat needs to be 224 square inches. The equation that represents the combined area is

Answer 1

The width of the mat around the photo is 3 inches

The combined area of the of the photo and math = 224 square inches

The combined area is represented as:

(2w +8)(2w + 10) = 224

Expand the equation using the distributive rule

$4w^2+20w+16w+80=224\\\\4w^2+36w+80-224=0\\\\4w^2+36w-144=0$

Divide through by 4

$w^2+9w-36=0$

Factorize the resulting quadratic equation to solve for w

$w^2-3w+12w-36=0\\\\w(w-3)+12(w-3)=0\\\\(w-3)(w+12)=0$

w  -  3  =  0

w   =  3

w  +  12  =  0

w   =  -12

The width of the mat around the photo is 3 inches

Learn more on area here: brainly.com/question/20968176

Answer 2

The width of the mat around the photo is 3 inches

Combined area:

2w +8)(2w + 10) = 224

where,

w = width of the mat around the photo

(2w +8)(2w + 10) = 224

open parenthesis

4w² + 20w + 16w + 80 = 224

4w² + 36w + 80 - 224 = 0

4w² + 36w - 144 = 0

divide through by 4

w² + 9w - 36 = 0

solve quadratic equation using factorization method

w² + 12w - 3w - 36 = 0

w(w + 12) - 3(w + 12) = 0

(w + 12) (w - 3) = 0

w + 12 = 0 or w - 3 = 0

w = -12 or w = 3

The width of the mat around the photo cannot be a negative value.

Therefore, the width of the mat around the photo is 3 inches

Learn more about quadratic equation:

brainly.com/question/1214333