Arug 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?

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
 

The border can be 4 ft or 19.5 ft