A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 23 feet by 25 feet and the area of the rug is 288 square feet, how wide will the border be
A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 16 feet by 25 feet and the area of the rug is 220 square feet, how wide will the border : Let x = the width of the border around the rug then (25-2x) by (16-2x) the dimensions of the rug : The area equation (25-2x)*(16-2x) = 220 sq/ft FOIL 400 - 50x - 32x + 4x^2 = 220 : Arrange as a quadratic equation 4x^2 - 82x + 400 - 220 = 0 : 4x^2 - 82x + 180 = 0 Simplify, divide by 2 2x^2 - 41x + 90 = 0 Factor (2x - 5)(x - 18) = 0 Two solutions 2x = 5 x = 2.5 ft and x = 18 ft, obviously this not the solution ; Border will be 2.5 ft
