A border of uniform width is placed around a rectangular photograph that measures 8 inches by 10 inches. If the area of the border is 144 square inches, what is the width of the border, in inches?

Answer:width of the border is 3 inchesStep-by-step explanation:Given data size = 8 inches by 10 inchesarea = 144 square inchesto find out width of the bordersolutionfirst we consider width of border is xarea of new full rectangle =  (8 + 2x ) × ( 10 + 2x )so we know  area of photo = 8 × 10 = 80 square inchesand area of border = 144 square inches that is givenso new area of photo with the border is 80 + 144 = 224 square inchesand we can say that area of full rectangle  - area of the photograph = Area of Border (8 + 2x) × (10 + 2x) – (80) = 144  square inches 80 + 16x + 20x + [tex]4x^{2}[/tex] – 80 = 144 [tex]4x^{2}[/tex] + 36x – 144 = 0 solve thios equation we get   [tex]2x^{2}[/tex] + 9x – 36 = 0 solve thios equation we get  (x + 12) (x – 3) = 0  so here x have two value one is negative and other is positiveso we consider only positive value x = -12 or x = 3width of the border is 3 inches