The width of a photo is 5 inches less than its length. A border of 2 inches is placed around the photo. The area covered by the photo and its border is 104 square inches. Find the dimensions of the photo itself

Answer:Dimensions of photo excluding border:x = 11 inchesy = 6 inches Step-by-step explanation:Let the length be 'x' and width be 'y'.The width of a photo is 5 inches less than its length, that is:x-5 = ylet 'X' be length of photo including border and 'Y' be the width of photo including border:Where X = x+2 and Y = y+2Now , we have X-5 = Yand X*Y = 104 square inches*putting Y = X-5*X(X-5) = 104[tex]X^2 - 5X - 104 = 0[/tex][tex]X^2 - 13X + 8X - 104 = [/tex][tex]X(X-13)+8(X-13) = 0\\(X-13)(X+8)[/tex]⇒ X-13 = 0          or        X+8 = 0Hence X = 13       or X = -8As length can not be negative, X = 13 inchesY = X-5 = 13-5 = 8 inchesDimensions of photo excluding border:x = X - 2 = 13-2 = 11 inchesy = Y-2   =  8-2 =  6 inches