Cynthia Besch wants to buy a rug for a room that is 6 ft wide and 15 ft long. She wants to leave a uniform strip of floor
around the rug. She can afford to buy 22 square feet of
carpeting. What dimensions should the rug have?
6 ft
22 ft
15 ft
Multiply.
4x2 - 42x +90 = 22
Write the equation in standard form.
4x2 - 42x + 68 = 0
Divide by 2, the greatest common factor of the coefficients.
2x2 - 21x +34 = 0
Next, factor. (The quadratic equation could also be solved by using the quadratic formula.)
(x-2)(2x - 17) = 0
By the principle of zero products, the first factor is 2; the second factor is 8.5.
Since the length, 15-2x, and the width, 6 - 2x, of the rug can't be negative, a uniform strip of floor around the rug is
2 ft.
Therefore, the rug should have the dimensions 11, 2.