Problema Solution
Cynthia Besch wants to buy a rug for a room that is 21 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 442 square feet of carpeting. What dimensions should the rug have?
Answer provided by our tutors
let
x = the width of the uniform strip around the rug
30 - 2x = the length of the rug
21 - 2x = the width of the rug
She can afford to buy 442 square feet of carpeting
(30 - 2x)(21 - 2x) = 442
by solving the quadratic equation we find 2 roots
x1 = 23.5 ft can not be the solution we need since the strip can not be bigger then the width of the room (21 ft)
x = 2 ft is the solution we are looking for
click here to see the step by step solution of the quadratic equation
l = 30 - 2*2 = 26 ft
w = 21 - 2*2 = 17 ft
the dimensions of the rug are 26 ft and 17 ft.