a girl wants to buy a rug for a room that is 21 ft wide and 22 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 132 square feet of carpeting. what dimensions should the rug have? how many ft?
The Area of the room = 21 x 22 = 462 sq.m The Rug should leave uniform strip therefor from all sides equal length must be cut off... So let length to be cut from one side be = x/2 So the Rug's sides will be = (21-x) and (22-x) So the area of the Rug will be equal to = (21-x)(22-x) (=132sq.m) = 22x21 - 21x - 22x + x^2 = 132 = x^2 - 43x +43 - 132 = 0 = x^2 - 43x + 330 = 0 Now Middle term Splitting = x^2 - (33 + 10)x +330 = 0 = x^2 - 33x - 10x + 330 = 0 = x (x-33) - 10 (x-33) = 0 = (x-10) (x-33) = 0 Either x= 10 or x=33 x cannot be equal to 33 as the max value could be only 21... So the dimensions of the rug are.. L= 11 B=12.. Thankyou.. Have a nice Day.. :)
In order for the strip of floor to be even around the rug, the length of the rug must be 1 ft longer than its width (to match the floor). So, here's what we know: W = x L = x + 1 A = 132 (area) Just write an equation for Area. LW = A Plug in your numbers x(x + 1) = 132 x^2 + x = 132 x^2 + x = 121 + 11 x^2 + x = 11^2 + 11 x = 11 Therefore: Width = 11 Length = 12
(21-2x)(22 -2x) =<132 21*22 -42x -44x +4x^2<=132 462-86x +4x^2 <=132 4x^2 -86x +330 <=0 2x^2 -43x +165 <=0 2x^2 -10x -33x+165<=0 2x(x-5) -33(x-5)<=0 (2x-33)(x-5)<=0 x =5..................Ans Hence strip of 5 ft is left Then dimension should be Length =22-10 =12 feet ......................Ans Width =21 -10 =11 feet .......................Ans Area of rug will be =12x11 =132 feet
