Question

A 15 -inch by 12-inch (width by length) picture is surrounded by a border of uniform width. The total area of the picture with the border around it is 418 in

Answer 1

Let the width of the border be x inches. Then the width and the length of the picture, with the border around it, are x+15 and x +12 inches respectively. Now, since the total area of the picture, with the border around it, is 416 sq. inches, hence (x+15)(x+12) = 418 or, x² +27x + 180 = 418 or, x² +27x – 238 = 0. On using the quadratic formula, we have x = [27±?{(27)² -4*1*(-238)}/2*1 = [27±?(729+952)]/2 = (27±?1681)/2 = (27±41)/2. Now, since x cannot be negative, we have x = (27+41)/2 = 68/2 = 34 inches. Hence the border of uniform width 34 inches.