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 22 feetby 25 feet and the area of the rug is 238 square feet, how wide will the border be?
Accepted Solution
A:
-------------------------------------------------------- Find area of the border : -------------------------------------------------------- Area of the room = 22 x 25 = 550 ft² Area of the rug = 238 ft² Area of the border = 550 - 238 = 312 ft²
-------------------------------------------------------- Define y: -------------------------------------------------------- Let the width be y.
-------------------------------------------------------- Find area of the border in term of y : -------------------------------------------------------- The area of the border = 22y x 2 + 25y x 2 - 4y² = 94y - 4y² *We need to take away 4y² because the 4 corners will be overlap twice if we don't.
-------------------------------------------------------- Solve y : -------------------------------------------------------- 94y - 4y² = 312 4y² - 94y + 312 = 0 2y² - 47y + 156 = 0 (y - 4)(2y - 39) = 0 y = 4 or y = 19.5
-------------------------------------------------------- Answer: The border can be 4 ft or 19.5 ft --------------------------------------------------------