math homework please help

Question

Cynthia Besch wants to buy a rug for a room that is 27 ft wide and 35 ft long. she wants to leave a uniform strip of the floor around the rug. she can afford to buy 425 square feet of carpeting. what dimensions should the rug have?

Answer 1

(27-2x)(35-2x) = 35(27) -425

945 -124x + 4x^2 = 945 -425

4x^2 -124x +425 = 0

x^2 -31x = -425/4

x = 31/2 + or - .5sqr(961 -4(106.25) = 15.5 + or - 11.6 = 3.9

x = about 3.9 ft

dimensions are 27-7.8 by 35-7.8

= about 19.2 feet by 27.2 feet

27(35) = 945 ft^2

19.2(27.2) = 522.24 ft^2

945 -522.24 = 423, close to 425, given rounding errors