If a rectangle has length 2x and width x, and the area is 18, what is x?

• A. x = -3
• B. x = -1
• C. x = 1
• D. x = 3

Answer: (D)

Area comes from multiplying the sides. For this rectangle, length is 2x and width is x, so the area is (2x)(x) = 2x^2. If that area is 18, then 2x^2 = 18, which gives x^2 = 9. This gives x = 3 or x = -3. Since a rectangle’s side lengths must be nonnegative, we take the positive value. With x = 3, the dimensions are 6 by 3, and the area is 6×3 = 18. So x = 3.