Question

Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 30 ft long. She wants to leave a uniform strip of floor around the rug. She can afford 390 square feet of carpeting. What dimensions should the rug have?

Answer 1

width=15ft

lenght=26 ft

Explanation:

(19-2x)(30-2x)=390.

570-38x-60+4x to the second power=390

combine likes terms:

4x to the second power-98+570=390

Answer 2

width = 15 ft

length = 26 ft

Explanation:

(19 - 2x)(30 - 2x) = 390

570 - 38x - 60x + 4x² = 390

combine like terms:

4x² - 98x + 570 = 390

subtract 390 from each side of the equation:

4x² - 98x + 180 = 0

divide by 4:

x² - 24.5 + 45 = 0

(x - 22.5)(x - 2) = 0

x = 22.5 and x = 2

since x = 22.5 is out of the usable range, x = 2 ft is the solution

width = 19 ft - 4 ft = 15 ft (remember that there will be a 2 ft gap at each wall, thus subtract 4 ft)

length = 30 ft - 4 ft = 26 ft